%  File:  all_brec.bib              Updated:  07-JUL-1992
%
% Automatic Differentiation Bibliography,
% collected by George F. Corliss,
% in Automatic Differentiation of Algorithms: 
%    Theory, Implementation, and Application,
% Andreas Griewank and George Corliss (eds.),
% SIAM, Philadelphia, Penn., 1991.
%
% Assumes commands to get Russian digraphs:
%   \newcommand{\Yu}{{Yu}}
%   \newcommand{\Ye}{{Ye}}
%   \newcommand{\Ju}{{Ju}}

@BOOK
{
   Aber88a,
   AUTHOR    = "Aberth, Oliver",
   TITLE     = "Precise Numerical Analysis",
   PUBLISHER = "William Brown",
   ADDRESS   = "Dubuque, Iowa",
   YEAR      = "1988",
   COMMENT   = "Text for a one semester, junior level course in numerical
                analysis.  Includes PC disk with software written in PBASIC.
                Sound introductory level discussion of code lists and error
                capture techniques.",
   KEYWORDS  = "general numerical analysis; interval techniques;
                differentiation arithmetic; variable precision arithmetic;
                linear algebra; differentiation; integration; ordinary
                differential equations.",
   ABSTRACT  = "Aberth addresses elementary issues of precise floating point
               computations using variable precision range arithmetic.
               Numbers are represented as a variable precision number $\pm$
               a range.  Rational arithmetic is also considered.  Chapters
               are devoted to \begin{enumerate} \item rootfinding, \item
               polynomial rootfinding, \item numerical linear algebra,
               \item differentiation and integration, and \item ordinary
               differential equations.\end{enumerate}  Differentiation is
               handled by a codelist approach like [Rall81a], and
               applications to Taylor series are given.  Interval
               techniques for ordinary differential equations are based on
               using an {\it a priori\/} bound to capture remainder terms.
               Several methods are illustrated, including Taylor series
               methods."
}


@BOOK
{
   Abra70a,
   EDITOR    = "Abramowitz, M.
                and Stegun, I. A.",
   TITLE     = "Handbook of Mathematical Functions",
   PUBLISHER = "Dover",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1970",
   REFERRED  = "[Layn91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Adam69a,
   AUTHOR    = "Adamson, D. S.
                and Winant, C. W.",
   TITLE     = "A {SLANG} Simulation of an Initially Strong Shock Wave 
                Downstream of an Infinite Area Change",
   BOOKTITLE = "Proceedings of the Conference on Applications of 
                Continuous-System Simulation Languages",
   PUBLISHER = "",
   YEAR      = "1969",
   PAGES     = "231--240",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MANUAL
{
   AdaLRM,
   AUTHOR    = "{Ada Joint Program Office}",
   TITLE     = "Reference Manual for the {A}da Programming Language,
                {ANSI/MIL--STD--1815A}",
   ORGANIZATION = "",
   ADDRESS   = "Washington, D.C.",
   YEAR      = "1983",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   AFNO83a,
   AUTHOR    = "AFNOR",
   TITLE     = "Le Langage de Programmation {FORTRAN}",
   INSTITUTION = "{A}ssociation {F}ran\c{c}aise de {N}ormalisation, {T}our 
               {E}urope, {C}edex 7, {F}-92080 {P}aris {L}a {D}efense {C}edex,
               France",
   YEAR      = "1983",
   TYPE      = "norme {I}{S}{O} 1539 (norme {N}{F} {Z} 65-110)",
   NUMBER    = "",
   ADDRESS   = "",
   REFERRED  = "[Soul91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Ahoa86a,
   AUTHOR    = "Aho, A. V. 
                and Sethi, R
                and Ullman, J. D.",
   TITLE     = "Compilers: {P}rinciples, Techniques, and Tools",
   PUBLISHER = "Addison-Wesley",
   SERIES    = "",
   ADDRESS   = "Reading, Mass.",
   YEAR      = "1986",
   REFERRED  = "[Thac91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Aida89a,
   AUTHOR    = "Aida-Zade, K. R.
                and Evtushenko, {\Yu}ri G.",
   TITLE     = "Bystroe avtomaticheskoe differentsirovanie na {{\`{E}}{V}{M}}
                ({F}ast Automatic Differentiation)",
   JOURNAL   = "Matematicheskoe Modelirovanie
                (Mathematical Modelling)",
   VOLUME    = "1",
   NUMBER    = "",
   YEAR      = "1989",
   PAGES     = "121--139",
   REFERRED  = "[Evtu91a]; [Irim91a].",
   NOTE      = "(In Russian).",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Alef83a,
   AUTHOR    = "Alefeld, G.
                and Herzberger, J.",
   TITLE     = "Introduction to Interval Computations",
   PUBLISHER = "Academic Press",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1983",
   REFERRED  = "[Irim91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Ande79a,
   AUTHOR    = "Anderson, L.
                and Ibragimov, Nail~H.",
   TITLE     = "Lie-Backlund Transformations in Applications",
   PUBLISHER = "SIAM",
   SERIES    = "Studies in Applied Mathematics",
   ADDRESS   = "Philadelphia, Penn.",
   YEAR      = "1979",
   REFERRED  = "[Mich91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Arbe86a,
   AUTHOR    = "Arbenz, P.
                and Gander, W.",
   TITLE     = "Solving nonlinear eigenvalue problems by algorithmic
               differentiation",
   JOURNAL   = "Computing",
   VOLUME    = "36",
   YEAR      = "1986",
   PAGES     = "205--215",
   KEYWORDS  = "nonlinear eigenvalue problems; differentiation arithmetic;
                numerical results.",
   ABSTRACT  = "The eigenvalues of a matrix $A(\lambda)$ can be found by a
                zero finding method applied to the determinant function
                $det(A(\lambda))$.  The derivatives of $det(A(\lambda))$ can be
                found by differentiation arithmetic.  The paper presents
                such an algorithm.  Various numerical examples are provided
                and timing comparisons are given.",
}


@BOOK
{
   Arbi87a,
   AUTHOR    = "Arbib, M.",
   TITLE     = "Brains, Machines, and Mathematics",
   PUBLISHER = "Springer Verlag",
   SERIES    = "",
   ADDRESS   = "Berlin",
   YEAR      = "1987",
   REFERRED  = "[Saar91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Ball69a,
   AUTHOR    = "Ball, William E.",
   TITLE     = "{BSOLVE}: {S}olution to a set of nonlinear
                equations by {M}arquardt's method",
   BOOKTITLE = "Material and Energy Balance Computations",
   YEAR      = "1969",
   EDITOR    = "Henley, Ernest J.
                and Rosen, Edward M.",
   PUBLISHER = "John Wiley and Sons",
   ADDRESS   = "New York",
   PAGES     = "560--566",
   REFERRED  = "[Soul91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Ball73a,
   AUTHOR    = "Ball, William E.",
   TITLE     = "The {BSOLVE} subroutine",
   BOOKTITLE = "Optimization Techniques with {FORTRAN}",
   YEAR      = "1973",
   EDITOR    = "Kuester, James L.
                and Mize, Joe H",
   PUBLISHER = "McGraw-Hill",
   ADDRESS   = "New York",
   PAGES     = "240--250",
   REFERRED  = "[Soul91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Bard74a,
   AUTHOR    = "Bard, Y.",
   TITLE     = "Nonlinear Parameter Estimation",
   PUBLISHER = "Academic Press",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1974",
   REFERRED  = "[Garc91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Bart89a,
   AUTHOR    = "Bartholomew-Biggs, M. C.
                and Dixon, Lawrence C. W.
                and Maany, Z.
                and Mohseninia, M.",
   TITLE     = "Three Papers on Automatic Differentiation
                Presented at the {IFAC} {S}ymposium 
                on ``{D}ynamic {M}odelling \& {C}ontrol of {N}ational 
                {E}conomies,'' {J}uly 1989, {E}dinburgh, {S}cotland",
   TYPE      = "Technical Report",
   NUMBER    = "No. 223",
   INSTITUTION = "The Numerical Optimisation Center, Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   YEAR      = "1988",
   PAGES     = "",
   REFERRED  = "",
   COMMENT   = "",
   NOTE      = "Contains Automatic Differentiation of Large Sparse Systems,
                Automatic Differentiation and Constrained Optimization, and
                Parallel Automatic Differentiation in Ada Applied to the
                Navier Stokes Equations.",
   KEYWORDS  = "point algorithm; differentiation arithmetic; optimisation.",
   ABSTRACT  = "It is shown how the extended operations set of Ada can be
                used to allow automatic differentiation to be specified in a
                natural way.  This is then applied to solving optimisation
                problems using the truncated Newton method, see [Dixo86a]."
}



@ARTICLE
{
   Bart80a,
   AUTHOR    = "Barton, David",
   TITLE     = "On {T}aylor series and stiff equations",
   JOURNAL   = "ACM Trans. Math. Software",
   VOLUME    = "6",
   NUMBER    = "3",
   YEAR      = "1980",
   PAGES     = "280--294",
   REFERRED  = "MR 82e 65078; [Corl82a]; [Gupt85a]; [Hali83a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; Taylor series; stiff; automatic
                differentiation.",
   ABSTRACT  = "Surveys the work of Barton, Willers, and Zahar on Taylor series
                methods.  Gives a predictor-corrector algorithm based on Taylor
                series.  Parts: \begin{enumerate} \item Estimate the local
                error by matching the series at $ t_r $ and the series at
                $ t_{r+1} $ at the midpoint. \item Predict stepsize
                (iteratively) to achieve a fraction of the desired tolerance.
                This is very expensive. \item The predictor formula is an
                ordinary Taylor polynomial.  The corrector formula uses
                eigenvalues of the Jacobian to distort the series at
                $ t_{r+1} $ to compute the actual local contributions of the
                transients. \item Determine the order of the series. \item
                Detect when a transient has died away, or when it has
                reappeared.\end{enumerate}  A preprocessor written in PL/1
                uses automatic differentiation to write a Fortran program which
                uses recurrence relations to compute the series."
}


@ARTICLE
{
   Bart70a,
   AUTHOR    = "Barton, David
                and Willers, I. M.
                and Zahar, R. V. M.",
   TITLE     = "The automatic solution of ordinary differential equations by
                the method of {T}aylor series.",
   JOURNAL   = "Computer J.",
   VOLUME    = "14",
   NUMBER    = "3",
   YEAR      = "1970",
   PAGES     = "243--248",
   REFERRED  = "[Aber88a]; [Chan74a]; [Chan86a]; [Corl82a];
                [Fisc87e]; [Hans80a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithms; Taylor series; computer languages;
                differentiation arithmetic.",
   ABSTRACT  = "The paper presents a simple langauge for the specification
                of mixed algebraic-ordinary differential systems with
                initial conditions.  The language is specified in a BNF-type
                form.  It is shown how to compile and optimise this
                language.  The authors then apply the automatic
                differentiation technique of [Moor66a] to generate the
                Taylor series solution of a system specified in this
                language.  Some simple examples of the language are given,
                but no numerical results are provided."
}


@INCOLLECTION
{
   Bart71a,
   AUTHOR    = "Barton, David
                and Willers, I. M.
                and Zahar, R. V. M.",
   TITLE     = "Taylor Series Methods for Ordinary Differential Equations
                -- {A}n Evaluation",
   BOOKTITLE = "Mathematical Software",
   YEAR      = "1971",
   EDITOR    = "Rice, John",
   PUBLISHER = "Academic Press",
   ADDRESS   = "New York",
   PAGES     = "369--390",
   REFERRED  = "[Fisc87e].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Baue74a,
   AUTHOR    = "Bauer, F. L.",
   TITLE     = "Computational graphs and rounding errors",
   JOURNAL   = "SIAM J. on Numerical Analysis",
   VOLUME    = "11",
   NUMBER    = "",
   YEAR      = "1974",
   PAGES     = "87--96",
   REFERRED  = "[Char91a]; [Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Baur83a,
   AUTHOR    = "Baur, W.
                and Strassen, V.",
   TITLE     = "The Complexity of Partial Derivatives",
   JOURNAL   = "Theoretical Computer Science",
   VOLUME    = "22",
   YEAR      = "1983",
   PAGES     = "317--330",
   REFERRED  = "[Gold91a]; [Irim91a]; [Kubo91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Beck88a,
   AUTHOR    = "Becker, Richard A.
                and Chambers, John M.
                and Wilks, Allan R.",
   TITLE     = "The New {S} Language",
   PUBLISHER = "{Wadsworth and Brooks/Cole}",
   SERIES    = "Computer Science Series",
   ADDRESS   = "Pacific Grove, Calif.",
   YEAR      = "1988",
   REFERRED  = "[Corl91a].",
}


@TECHREPORT
{
   Beda59a,
   AUTHOR    = "Beda, L. M.
                and Korolev, L. N.
                and Sukkikh, N. V.
                and Frolova, T. S.",
   TITLE     = "Programs for automatic differentiation for the machine {BESM}",
   TYPE      = "{T}echnical {R}eport",
   NUMBER    = "",
   INSTITUTION = "Institute for Precise Mechanics and Computation Techniques,
                Academy of Science",
   ADDRESS   = "Moscow, USSR",
   YEAR      = "1959",
   REFERRED  = "[Fisc87e]; [Grie91e]; [Ostr71a].",
   NOTE      = "(In Russian).",
   COMMENT   = "Seems to be the earliest paper on the subject -- Fischer.",
   KEYWORDS  = "differentiation arithmetic; computer program.",
   ABSTRACT  = "",
}


@BOOK
{
   Bell65b,
   AUTHOR    = "Bellman, R. E.
                and Kalaba, Robert E.",
   TITLE     = "Quasilinearization and Nonlinear Boundary Value Problems",
   PUBLISHER = "American Elsevier Publishing Co.",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1965",
   REFERRED  = "[Tham91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Bell65a,
   AUTHOR    = "Bellman, R. E.
                and Kagiwada, Harriet H.
                and Kalaba, Robert E.",
   TITLE     = "{W}engert's Numerical Method for Partial Derivatives,
                Orbit Determination, and Quasilinearization",
   JOURNAL   = "Comm. ACM",
   YEAR      = "1965",
   VOLUME    = "8",
   NUMBER    = "4",
   PAGES     = "231--232",
   REFERRED  = "[Fisc87e]; [Kala83a]; [Tesf91a]",
   COMMENT   = "This is a comment on Wengert's paper, see [Weng64a].",
   KEYWORDS  = "point algorithms; partial derivatives.",
   ABSTRACT  = "The method presented in [Weng64a] is tested on specific
                problem.  It is shown that the method is valid for this
                specific problem.",
}


@TECHREPORT
{
   Berz87a,
   AUTHOR    = "Berz, Martin",
   TITLE     = "The Differential Algebra {FORTRAN} Precompiler {DAFOR}",
   INSTITUTION = "Los Alamos National Laboratory",
   ADDRESS   = "Los Alamos, N.M.",
   TYPE      = "Technical Report AT--3",
   NUMBER    = "TN--87--32",
   MONTH     = "",
   YEAR      = "1987",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Berz87b,
   AUTHOR    = "Berz, Martin",
   TITLE     = "The method of power series tracking for the mathematical 
                description of beam dynamics",
   JOURNAL   = "Nuclear Instruments and Methods",
   VOLUME    = "A258",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1987",
   PAGES     = "431 +",
   REFERRED  = "[Berz91a]; [Mich91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Berz88a,
   AUTHOR    = "Berz, Martin",
   TITLE     = "{D}ifferential algebraic description and analysis of 
                trajectories in vacuum electronic devices including 
                spacecharge effects",
   JOURNAL   = "IEEE Transactions on Electron Devices",
   VOLUME    = "53",
   NUMBER    = "11",
   MONTH     = "",
   YEAR      = "1988",
   PAGES     = "2002 +",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Berz88b,
   AUTHOR    = "Berz, Martin",
   TITLE     = "Differential Algebraic Treatment of Beam Dynamics 
                to Very High Orders including Applications to Spacecharge",
   JOURNAL   = "AIP Conference Proceedings",
   VOLUME    = "177",
   NUMBER    = "",
   YEAR      = "1988",
   PAGES     = "275 +",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Berz89a,
   AUTHOR    = "Berz, Martin",
   TITLE     = "Differential Algebraic Description of Beam Dynamics 
                to Very High Order",
   JOURNAL   = "Particle Accelerators",
   VOLUME    = "24",
   NUMBER    = "",
   YEAR      = "1989",
   PAGES     = "109",
   REFERRED  = "[Berz91a]; [Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Berz89b,
   AUTHOR    = "Berz, Martin",
   TITLE     = "Differential algebra -- {A} new tool",
   BOOKTITLE = "Proceedings of the 1989 IEEE Particle Accelerator 
                Conference",
   YEAR      = "March 20--23, 1989",
   EDITOR    = "Bennet, Floyd
                and Kopta, Joyce",
   PUBLISHER = "IEEE",
   ADDRESS   = "",
   PAGES     = "",
   REFERRED  = "[Mich91a].",
   COMMENT   = "IEEE Catalog Number 89CH2669-0",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Berz89c,
   AUTHOR    = "Berz, Martin",
   TITLE     = "The Description of Particle Accelerators using High Order
                Perturbation Theory on Maps",
   BOOKTITLE = "Physics of Particle Accelerators, vol. 1",
   VOLUME    = "",
   YEAR      = "1989",
   EDITOR    = "M. Month",
   PUBLISHER = "American Institute of Physics",
   ADDRESS   = "",
   PAGES     = "961 +",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Berz90a,
   AUTHOR    = "Berz, Martin",
   TITLE     = "Differential Algebra Precompiler Version 3 ---
                {R}eference Manual",
   INSTITUTION = "National Superconducting Cyclotron Laboratory, 
                  Michigan State University",
   TYPE      = "Technical Report",
   NUMBER    = "MSUCL -- 755",
   ADDRESS   = "East Lansing, Mich.",
   YEAR      = "1990",
   REFERRED  = "[Berz91a]; [Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = ""
}


@TECHREPORT
{
   Berz90b,
   AUTHOR    = "Berz, Martin",
   TITLE     = "{COSY} {INFINITY} Version 3 Reference Manual",
   INSTITUTION = "National Superconducting Cyclotron Lab., 
                  Michigan State University",
   TYPE      = "Technical Report",
   NUMBER    = "MSUCL -- 751",
   ADDRESS   = "East Lansing, Mich.",
   YEAR      = "1990",
   REFERRED  = "[Berz91a]; [Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Berz90c,
   AUTHOR    = "Berz, Martin",
   TITLE     = "Computational Aspects of Design and Simulation: 
                {COSY} {INFINITY}",
   JOURNAL   = "Nuclear Instruments and Methods",
   VOLUME    = "A298",
   NUMBER    = "",
   YEAR      = "1990",
   PAGES     = "473 +",
   REFERRED  = "[Berz91a]; [Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Berz90d,
   AUTHOR    = "Berz, Martin",
   TITLE     = "{COSY} {INFINITY}, an arbitrary order general purpose 
                optics code",
   BOOKTITLE = "Computer Codes and the Linear Accelerator Community",
   YEAR      = "1990",
   EDITOR    = "",
   PUBLISHER = "Los Alamos LA--11857--C",
   ADDRESS   = "",
   PAGES     = "137 +",
   REFERRED  = "[Berz91a]; [Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = ""
}


@ARTICLE
{
   Berz90e,
   AUTHOR    = "Berz, Martin",
   TITLE     = "Arbitrary order description of arbitrary particle 
                optical systems",
   JOURNAL   = "Nuclear Instruments and Methods",
   VOLUME    = "A298",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1990",
   PAGES     = "426 +",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Berz90f,
   AUTHOR    = "Berz, Martin",
   TITLE     = "The {DA} precompiler {DAFOR}",
   INSTITUTION = "Lawrence Berkeley National Laboratory",
   MONTH     = "",
   YEAR      = "1990",
   TYPE      = "{T}echnical {R}eport",
   NUMBER    = "",
   ADDRESS   = "Berkeley, Calif.",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Berz91a,
   AUTHOR    = "Berz, Martin",
   TITLE     = "Forward Algorithms for High Orders and Many Variables
                with Application to Beam Physics",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "147--156",
   REFERRED  = "[Flan91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Berz91b,
   AUTHOR    = "Berz, Martin",
   TITLE     = "{COSY} {INFINITY} Version 4 Reference Manual",
   INSTITUTION = "National Superconducting Cyclotron Lab., 
                  Michigan State University",
   TYPE      = "Technical Report",
   NUMBER    = "MSUCL -- 771",
   ADDRESS   = "East Lansing, Mich.",
   YEAR      = "1991",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = ""
}


@ARTICLE
{
   Berz91c,
   AUTHOR    = "Berz, Martin",
   TITLE     = "Automatic differentiation as an application of 
                nonarchimedean analysis",
   JOURNAL   = "IMACS Annals of Computing and Applied Mathematics",
   VOLUME    = "",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "in print",
   PAGES     = "",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Berz87c,
   AUTHOR    = "Martin Berz 
                and H.~Wollnik",
   TITLE     = "The program {HAMILTON} for the analytic solution of 
                the equations of motion in particle optical systems 
                through fifth order",
   JOURNAL   = "Nuclear Instruments and Methods",
   VOLUME    = "A258",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1987",
   PAGES     = "364 +",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Bigg71a,
   AUTHOR    = "Biggs, M. C.",
   TITLE     = "Minimization algorithms making use 
                of non-quadratic properties of the objective function",
   JOURNAL   = "J. the Institute of Mathematics and Its 
                Applications",
   VOLUME    = "8",
   NUMBER    = "",
   YEAR      = "1971",
   PAGES     = "315--327",
   REFERRED  = "[Garc91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Bigg73a,
   AUTHOR    = "Biggs, M. C.",
   TITLE     = "A note on minimization algorithms which make use of 
                non-quadratic properties of the objective function",
   JOURNAL   = "J. the Institute of Mathematics and Its 
                Applications",
   VOLUME    = "12",
   NUMBER    = "",
   YEAR      = "1973",
   PAGES     = "337--338",
   REFERRED  = "[Garc91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Bisc91a,
   AUTHOR    = "Bischof, Christian",
   TITLE     = "Issues in Parallel Automatic Differentiation",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "100--113",
   REFERRED  = "[Corl91a]; [Layn91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Bisc91b,
   AUTHOR    = "Bischof, Christian
                and Griewank, Andreas
                and Juedes, David",
   TITLE     = "Exploiting parallelism in automatic differentiation",
   BOOKTITLE = "Proceedings of the 1991 International Conference
                on Supercomputing",
   EDITOR    = "Elias Houstis
                and Yoichi Muraoka",
   PUBLISHER = "ACM Press",
   ADDRESS   = "Baltimore, Md.",
   YEAR      = "1991",
   PAGES     = "146--153",
   NOTE      = "Also appeared as Preprint MCS--P204--0191,
                Mathematics and Computer Science Division,
                Argonne National Laboratory,
                Argonne, Ill., January 1991.",
   REFERRED  = "[Bisc91a].",
}


@TECHREPORT
{
   Bisc91c,
   AUTHOR    = "Bischof, Christian
                and Hu, James",
   TITLE     = "Utilities for Building and Optimizing a Computational
                Graph for Algorithmic Decomposition",
   INSTITUTION = "Mathematics and Computer Sciences Division, 
                Argonne National Laboratory",
   YEAR      = "1991",
   TYPE      = "Technical Memorandum",
   NUMBER    = "ANL/MCS--TM--148",
   ADDRESS   = "Argonne, Ill.",
   MONTH     = "April",
   NOTE      = "",
   REFERRED  = "[Bisc91a].",
}



@TECHREPORT
{
   Bisc91f,
   AUTHOR = "Christian Bischof
             and Alan Carle
             and George Corliss
             and Andreas Griewank
             and Paul Hovland",
   TITLE  = "Generating Derivative Codes from {F}ortran Programs",
   INSTITUTION = "Mathematics and Computer Science Division,
             Argonne National Laboratory",
   MONTH     = "February",
   YEAR      = "1992",
   TYPE      = "Preprint",
   NUMBER    = "MCS--P263--0991",
   ADDRESS   = "Argonne, Ill.",
   NOTE      = "Also appeared as Technical Report 91185,
                Center for Research in Parallel Computation,
                Rice University, Houston, Tex.",
   REFERRED  = "[Bisc91g]; [Bisc91h].",
   COMMENT   = "Working Note \# 1",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Bisc92c,
   AUTHOR = "Christian Bischof
             and Alan Carle
             and George Corliss
             and Andreas Griewank
             and Paul Hovland",
   TITLE  = "Generating Derivative Codes from {F}ortran Programs",
   JOURNAL   = "Scientific Computing",
   VOLUME    = "",
   NUMBER    = "",
   YEAR      = "to appear",
   PAGES     = "",
   NOTE      = "ADIFOR Working Note \# 1.
                Also appeared as Preprint MCS--P263--0991,
                Mathematics and Computer Science Division,
                Argonne National Laboratory, Argonne, Ill.,
                September 1991, and as Technical Report 91185,
                Center for Research in Parallel Computation,
                Rice University, Houston, Tex., 1991.",
   REFERRED  = "[Bisc91g]; [Bisc91h].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Bisc91g,
   AUTHOR = "Christian Bischof
             and Paul Hovland",
   TITLE  = "Using {ADIFOR} to Compute Dense and Sparse {J}acobians",
   INSTITUTION = "Mathematics and Computer Science Division,
             Argonne National Laboratory",
   MONTH     = "October",
   YEAR      = "1991",
   TYPE      = "Technical Memorandum",
   NUMBER    = "ANL/MCS--TM--158",
   ADDRESS   = "Argonne, Ill.",
   NOTE      = "ADIFOR Working Note \# 2.",
   REFERRED  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Bisc92a,
   AUTHOR = "Christian Bischof
             and George Corliss
             and Andreas Griewank",
   TITLE  = "{ADIFOR} Exception Handling",
   INSTITUTION = "Mathematics and Computer Science Division,
             Argonne National Laboratory",
   MONTH     = "January",
   YEAR      = "1992",
   TYPE      = "Technical Memorandum",
   NUMBER    = "ANL/MCS--TM--159",
   ADDRESS   = "Argonne, Ill.",
   NOTE      = "ADIFOR Working Note \# 3.",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Bisc91j,
   AUTHOR = "Christian Bischof
             and Alan Carle
             and George Corliss
             and Andreas Griewank
             and Paul Hovland",
   TITLE  = "{ADIFOR}: {F}ortran Source Translation for Efficient 
             Derivatives",
   INSTITUTION = "Mathematics and Computer Science Division,
             Argonne National Laboratory",
   MONTH     = "December",
   YEAR      = "1991",
   TYPE      = "Preprint",
   NUMBER    = "MCS--P278--1291",
   ADDRESS   = "Argonne, Ill.",
   NOTE      = "ADIFOR Working Note \# 4.",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Bisc92b,
   AUTHOR = "Christian Bischof
             and Alan Carle
             and George Corliss
             and Andreas Griewank",
   TITLE  = "{ADIFOR}: Automatic Differentiation in a Source 
             Translation Environment",
   INSTITUTION = "Mathematics and Computer Science Division,
             Argonne National Laboratory",
   MONTH     = "January",
   YEAR      = "1992",
   TYPE      = "Preprint",
   NUMBER    = "MCS--P288--0192",
   ADDRESS   = "Argonne, Ill.",
   NOTE      = "ADIFOR Working Note \# 5.  
                Accepted for the International Symposium on Symbolic 
                and Algebraic Computation, 
                July 27--29, 1992, Berkeley, Calif.",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Bisc92d,
   AUTHOR = "Christian Bischof
             and George Corliss
             and Andreas Griewank",
   TITLE  = "Structured Second- and Higher-Order Derivatives Through 
             Univariate {T}aylor Series",
   INSTITUTION = "Mathematics and Computer Science Division,
               Argonne National Laboratory",
   MONTH     = "March",
   YEAR      = "1992",
   TYPE      = "Preprint",
   NUMBER    = "MCS--P296--0392",
   ADDRESS   = "Argonne, Ill.",
   NOTE      = "ADIFOR Working Note \# 6.",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Bisc92e,
   AUTHOR = "Christian Bischof
             and Moe El-Khadiri",
   TITLE     = "On Exploiting Partial Separability and Extending the 
                Compile-Time Reverse Mode in {ADIFOR}",
   INSTITUTION = "Mathematics and Computer Science Division,
               Argonne National Laboratory",
   MONTH     = "",
   YEAR      = "1992",
   TYPE      = "Technical Memorandum",
   NUMBER    = "ANL/MCS--TM--163",
   ADDRESS   = "Argonne, Ill.",
   NOTE      = "ADIFOR Working Note \# 7.",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Bohl87a,
   AUTHOR    = "Bohlender, G.
                and Ullrich, Ch.
                and Wolff von Gudenberg, J.
                and Rall, Louis B.",
   TITLE     = "{P}ascal-{SC}, A Computer Language for Scientific Computation",
   PUBLISHER = "Academic Press",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1987",
   REFERRED  = "[Kubo91a]; [Layn91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Bord56a,
   AUTHOR    = "Bordewijk, J. L.",
   TITLE     = "Inter-Reciprocity Applied to Electrical Networks",
   JOURNAL   = "Applied Science Research, The Netherlands, Sect. B",
   VOLUME    = "6",
   NUMBER    = "",
   YEAR      = "1956",
   PAGES     = "1--74",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Boyl90a,
   AUTHOR    = "Boyle, A.
                and Caviness, B. F.",
   TITLE     = "Future Directions for Research in Symbolic Computing",
   PUBLISHER = "SIAM",
   SERIES    = "",
   ADDRESS   = "Philadelphia, Penn.",
   YEAR      = "1990",
   REFERRED  = "[Gold91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Brac68a,
   AUTHOR    = "Bracken, J. 
                and McCormick, G. P.",
   TITLE     = "Selected Applications of Nonlinear Programming",
   PUBLISHER = "John Wiley and Sons",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1968",
   REFERRED  = "[Gayd91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Bram61a,
   AUTHOR    = "Bramhall, J. N.",
   TITLE     = "An iterative method for inversion of power series",
   JOURNAL   = "Comm. ACM",
   VOLUME    = "4",
   NUMBER    = "",
   YEAR      = "1961",
   PAGES     = "317--318, 503",
   REFERRED  = "[Laws91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Bren73a,
   AUTHOR    = "Brent, Richard P.",
   TITLE     = "Algorithms for Minimization without Derivatives",
   PUBLISHER = "Prentice-Hall",
   SERIES    = "",
   ADDRESS   = "Englewood Cliffs, N.J.",
   YEAR      = "1973",
   REFERRED  = "[Garc91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Bren77a,
   AUTHOR    = "Brent, Richard P. 
                and Kung, H. T.",
   TITLE     = "Fast algorithms for composition and reversion of 
                multivariate power series",
   BOOKTITLE = "Proceedings of the Conference on Theoretical
                Computer Science, University of Waterloo, Waterloo, 
                Ontario, Canada, August 1977",
   PUBLISHER = "",
   YEAR      = "1977",
   PAGES     = "149--158",
   REFERRED  = "[Laws91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Bren78a,
   AUTHOR    = "Brent, Richard P. 
                and Kung, H. T.",
   TITLE     = "Fast algorithms for manipulating formal power series",
   JOURNAL   = "J. ACM",
   VOLUME    = "25",
   NUMBER    = "4",
   YEAR      = "1978",
   PAGES     = "581--595",
   REFERRED  = "[Laws91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Bren80a,
   AUTHOR    = "Brent, Richard P. 
                and Traub, Joseph F.",
   TITLE     = "On the Complexity of Composition and Generalized Composition
                of Power Series",
   JOURNAL   = "SIAM J. Comput.",
   VOLUME    = "9",
   NUMBER    = "1",
   MONTH     = "February",
   YEAR      = "1980",
   PAGES     = "54--66",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}

@ARTICLE
{
   Broo83a,
   AUTHOR    = "Brooks, B. R. 
               and Bruccoleri, R. E. 
               and Olafson, B. D. 
               and States, D. J. 
               and Swaminathan, S.
               and Karplus, M.",
   TITLE     = "{CHARMM}: {A} Program for Macromolecular Energy, Minimization,
               and Dynamics Calculations",
   JOURNAL   = "J. Computational Chemistry",
   VOLUME    = "4",
   NUMBER    = "2",
   MONTH     = "",
   YEAR      = "1983",
   PAGES     = "187--217",
   REFERRED  = "[Gayd91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Broo88a,
   AUTHOR    = "Brook, A. 
                and Kendrick, D.
                and Meerhaus, A.",
   TITLE     = "{GAMS}: {A} User's Guide",
   PUBLISHER = "Scientific Press",
   SERIES    = "",
   ADDRESS   = "Redwood City, Calif.",
   YEAR      = "1988",
   REFERRED  = "[Gayd91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Brow64a,
   AUTHOR    = "Brown, K. L. 
                and Belbeoch, R. 
                and Bounin, P.",
   TITLE     = "First- and second-order magnetic optics matrix 
                equations for the midplane of uniform-field 
                wedge magnets",
   JOURNAL   = "Review of Scientific Instruments",
   VOLUME    = "35",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1964",
   PAGES     = "481 +",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Brow79a,
   AUTHOR    = "K.~L. Brown",
   TITLE     = "The Ion Optical Program {TRANSPORT}",
   INSTITUTION = "SLAC",
   MONTH     = "",
   YEAR      = "1979",
   TYPE      = "Technical Report",
   NUMBER    = "No. 91",
   ADDRESS   = "",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Breu69a,
   AUTHOR    = "Breuer, Melvin A.",
   TITLE     = "Generation of optimal code for expressions via 
                factorization",
   JOURNAL   = "Comm. ACM",
   VOLUME    = "12",
   NUMBER    = "6",
   YEAR      = "1969",
   PAGES     = "330--340",
   REFERRED  = "[Char91a]; [Gold91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Byrn87a,
   AUTHOR    = "Byrne, George D.
                and Hindmarsh, Alan C.",
   TITLE     = "Stiff {ODE} Solvers: {A} Review of Current and Coming
                Attractions",
   JOURNAL   = "J. Computational Physics",
   VOLUME    = "70",
   NUMBER    = "",
   YEAR      = "1987",
   PAGES     = "1--62",
   REFERRED  = "[Dixo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Cacu81a,
   AUTHOR    = "D. G. Cacuci",
   TITLE     = "Sensitivity Theory for Nonlinear Systems. {I}. {N}onlinear
                Functional Analysis Approach",
   JOURNAL   = "J. Math. Phys.",
   VOLUME    = "22",
   NUMBER    = "12",
   MONTH     = "",
   YEAR      = "1981",
   PAGES     = "2794--2802",
   REFERRED  = "[Bisc91g]; [Worl91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Cacu81b,
   AUTHOR    = "D. G. Cacuci",
   TITLE     = "Sensitivity Theory for Nonlinear Systems. {II}. {E}xtension to
                Additional Classes of Responses",
   JOURNAL   = "J. Math. Phys.",
   VOLUME    = "22",
   NUMBER    = "12",
   MONTH     = "",
   YEAR      = "1981",
   PAGES     = "2803--2812",
   REFERRED  = "[Bisc91g]; [Worl91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Cacu84a,
   AUTHOR    = "Cacuci, D. G. 
                and Hall, M. C. G.",
   TITLE     = "Efficient estimation of feedback effects with
                application to climate models",
   JOURNAL   = "J. Atmos. Sci.",
   VOLUME    = "41",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1984",
   PAGES     = "2063--2068",
   REFERRED  = "[Tala91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{ 
   Call88a,
   author    = "Callahan, D.
                and Cooper, K.
                and Hood, Robert T.
                and Kennedy, Ken
                and Torczon, Linda M.",
   title     = "{Para\-Scope}: {A} Parallel Programming Environment",
   journal   = "International J. Supercomputer Applications",
   volume    = 2, 
   number    = 4,
   month     = "December",
   year      = 1988,
   PAGES     = "",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MISC
{
   Camp92a,
   AUTHOR    = "Stephen L. Campbell
                and Edward Moore
                and Yangchun Zhong",
   TITLE     = "Utilization of Automatic Differentiation in Control 
                Algorithms",
   HOWPUBLISHED = "Preprint for presentation at the 31st IEEE Conference
                on Decision and Control to be held December 16--18, 1992,
                in Tucson.",
   YEAR      = "1992",
   PAGES     = "",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Care87a,
   AUTHOR    = "Carey, D. C.",
   TITLE     = "The Optics of Charged Particle Beams",
   PUBLISHER = "Harwood",
   SERIES    = "",
   ADDRESS   = "",
   YEAR      = "1987",
   REFERRED  = "[Berz91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Carl86a,
   AUTHOR    = "Carlile, Bradley R.",
   TITLE     = "Solution of nonlinear systems of equations on the 
                {FPS} 64-bit family of scientific computers using 
                automatic differentiation",
   BOOKTITLE = "Proceedings of the 1986 Array Conference (Portland, Oregon)",
   PUBLISHER = "",
   YEAR      = "1986",
   PAGES     = "142--169",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; differentiation arithmetic; nonlinear
                equations; numerical results; computer program.",
   ABSTRACT  = "The author considers the solution of nonlinear equations using
                Newton's method.  He presents a method which uses
                differentiation arithmetic to calculate the Jacobian which is
                required.  This method is compared with a finite differencing
                approach to calculating the Jacobian on a short pipeline
                machine, the FPS.  The differentiation arithmetic approach
                outperforms the finite differencing approach on all of the test
                problems presented solving two of the problems which the
                finite differencing approach failed to solve.",
}


@ARTICLE
{
   Cart74a,
   AUTHOR    = "Carter, R. D. 
                and {Kemp, Jr.}, L. F. 
                and Pierce, A. C. 
                and Williams, D. L.",
   TITLE     = "Performance Matching with Constraints",
   JOURNAL   = "Society of Petroleum Engineers J.",
   VOLUME    = "",
   NUMBER    = "",
   MONTH     = "April",
   YEAR      = "1974",
   PAGES     = "187--196",
   REFERRED  = "[Shah91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Chan67a,
   AUTHOR    = "Chang, Y. F.",
   TITLE     = "The Conduction-Diffusion Theory of Semiconductor
                Junctions",
   JOURNAL   = "J. Applied Physics",
   VOLUME    = "38",
   NUMBER    = "2",
   YEAR      = "1967",
   PAGES     = "534--544",
   REFERRED  = "[Corl91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Chan74a,
   AUTHOR    = "Chang, Y. F.",
   TITLE     = "Automatic solution of differential equations",
   BOOKTITLE = "Constructive and Computational Methods for Differential and
                Integral Equations",
   SERIES    = "Lecture Notes in Mathematics",
   VOLUME    = "430",
   EDITOR    = "Colton, D. L.
                and Gilbert, R. P.",
   PUBLISHER = "Springer Verlag",
   ADDRESS   = "New York",
   YEAR      = "1974",
   PAGES     = "61--94",
   REFERRED  = "[Chan86a]; [Corl82a]; [Corl88a]; [Hali83a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; Taylor series; automatic differentiation.",
   ABSTRACT  = "Compiler programs ATSCPL and ATSBVP are describes which accept
                as input up to 99 coupled 4th order differential equations
                described using simple Fortran statements.  The solution
                program uses the Taylor series method to solve the equations.
                The paper is a good introduction to the basics of numerical
                Taylor series methods such as step length control.  Various
                example problems are solved, and results are given."
}


@ARTICLE
{
   Chan86a,
   AUTHOR    = "Chang, Y. F.",
   TITLE     = "The {ATOMCC} Toolbox",
   JOURNAL   = "BYTE",
   VOLUME    = "11",
   NUMBER    = "4",
   YEAR      = "1986",
   PAGES     = "215--224",
   REFERRED  = "[Corl88a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; Taylor series; automatic differentiation.",
   ABSTRACT  = "ATOMCC is a pre-processor which accepts a Fortran-like
                statement of a system of ordinary differential equations and
                writes a Fortran object program which is run later to solve
                the system.  The object program uses recurrence relations to
                generate the series and a radius of convergence analysis to
                choose a stepsize which controls the local error.  The program
                also solves stiff systems.  It runs on IBM PC compatible
                computers up to large mainframes.",
}


@MISC
{
   Chan91a,
   AUTHOR    = "Chang, Y. F.",
   TITLE     = "A Variable-Order (10 -- $ \infty $) {T}aylor Series
                Method for Solving {ODE}'s with Integration Steps
                Almost Equal to the Radii of Convergence",
   HOWPUBLISHED = "Poster presented at {SIAM} {W}orkshop on
                {A}utomatic {D}ifferentiation of {A}lgorithms, 
                {B}reckenridge, Colo.",
   MONTH     = "January",
   YEAR      = "1991",
   REFERRED  = "[Corl91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Chan81a,
   AUTHOR    = "Chang, Y. F.
                and Tabor, Mike
                and Weiss, John
                and Corliss, George F.",
   TITLE     = "On the Analytic Structure of the {H}enon-{H}eiles
                System",
   JOURNAL   = "Physics Letters",
   VOLUME    = "85A",
   NUMBER    = "4",
   YEAR      = "1981",
   PAGES     = "211--213",
   REFERRED  = "[Corl91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Char91a,
   AUTHOR    = "Char, Bruce W.",
   TITLE     = "Computer Algebra as a Toolbox for Program Generation 
                and Manipulation",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "53--60",
   REFERRED  = "[Garc91a]; [Gold91a]; [Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Char86a,
   AUTHOR    = "Char, Bruce W.
                and Fee, G. J.
                and Geddes, Keith O.
                and Gonnet, Gaston H.
                and Monagan, Michael B.",
   TITLE     = "A Tutorial Introduction to {MAPLE}",
   JOURNAL   = "J. Symbolic Computation",
   VOLUME    = "2",
   NUMBER    = "2",
   YEAR      = "1986",
   PAGES     = "179--200",
   REFERRED  = "[Char91a]; [Gold91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Char88a,
   AUTHOR    = "Char, Bruce W.
                and Geddes, Keith O.
                and Gonnet, Gaston H.
                and Monagan, Michael B.
                and Watt, Stephen M.",
   TITLE     = "{MAPLE} Reference Manual",
   PUBLISHER = "Watcom Publications",
   ADDRESS   = "Waterloo, Ontario, Canada",
   YEAR      = "1988",
   REFERRED  = "[Corl91a]; [Gold91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Char91b,
   AUTHOR    = "Char, Bruce W.
                and Geddes, Keith O.
                and Gonnet, Gaston H.
                and Leong, Benton L.
                and Monagan, Michael B.
                and Watt, Stephen M.",
   TITLE     = "{M}aple {V} Language Reference Manual",
   PUBLISHER = "Springer Verlag",
   ADDRESS   = "New York",
   YEAR      = "1991",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Char91c,
   AUTHOR    = "Char, Bruce W.
                and Geddes, Keith O.
                and Gonnet, Gaston H.
                and Leong, Benton L.
                and Monagan, Michael B.
                and Watt, Stephen M.",
   TITLE     = "{M}aple {V} Library Reference Manual",
   PUBLISHER = "Springer Verlag",
   ADDRESS   = "New York",
   YEAR      = "1991",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Chav75a,
   AUTHOR    = "G. Chavent 
                and M. Dupuy 
                and P. Lemmonier",
   TITLE     = "History Matching by Use of Optimal Theory",
   JOURNAL   = "Society of Petroleum Engineers J.",
   VOLUME    = "",
   NUMBER    = "",
   MONTH     = "February",
   YEAR      = "1975",
   PAGES     = "74--86",
   REFERRED  = "[Shah91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Chao90a,
   AUTHOR    = "Chao, W. C.
                and Chang, L. P.",
   TITLE     = "Status of the development of a variational data
                assimilation system using the adjoint method at 
                {G}oddard {L}aboratory for {A}tmospheres",
   BOOKTITLE = "Proceedings of the International Symposium on Assimilation
                of Observations in Meteorology and Oceanography, World
                Meteorological Organization, Geneva, Switzerland",
   PUBLISHER = "",
   YEAR      = "1990",
   PAGES     = "355--358",
   REFERRED  = "[Tala91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Chen74a,
   AUTHOR    = "W. H. Chen  
                and G. R. Gavalas  
                and J. H. Seinfeld 
                and M. L. Wasserman",
   TITLE     = "A New Algorithm for Automatic History Matching",
   JOURNAL   = "Society of Petroleum Engineers J.",
   VOLUME    = "",
   NUMBER    = "",
   MONTH     = "December",
   YEAR      = "1974",
   PAGES     = "593--608",
   REFERRED  = "[Shah91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Chri91a,
   AUTHOR    = "Christianson, D. Bruce",
   TITLE     = "Automatic {H}essians by Reverse Accumulation in {A}da",
   JOURNAL   = "IMA J. on Numerical Analysis",
   VOLUME    = "",
   NUMBER    = "",
   YEAR      = "1991",
   PAGES     = "",
   NOTE      = "Presented at {SIAM} {W}orkshop on
                {A}utomatic {D}ifferentiation of {A}lgorithms, 
                {B}reckenridge, Colo., January 1991",
   REFERRED  = "[Corl91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Chri91b,
   AUTHOR    = "Christianson, D. Bruce",
   TITLE     = "Reverse Accumulation and Accurate Rounding Error Estimates
                for {T}aylor Series Coefficients",
   JOURNAL   = "Optimization Methods and Software",
   VOLUME    = "1",
   NUMBER    = "1",
   YEAR      = "1991",
   PAGES     = "81--94",
   NOTE      = "Also appeared as Technical Report No. NOC TR239,
                The Numerical Optimisation Centre, 
                University of Hertfordshire, U.K., July 1991",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Chri92a,
   AUTHOR    = "Christianson, D. Bruce",
   TITLE     = "Automatic {H}essians by reverse accumulation",
   JOURNAL   = "IMA J of Numerical Analysis ",
   VOLUME    = "12",
   NUMBER    = "",
   YEAR      = "1992",
   PAGES     = "135--150",
   NOTE      = "Also appeared as Technical Report No. NOC TR228,
                The Numerical Optimisation Centre, 
                University of Hertfordshire, U.K., April 1990",
   REFERRED  = "[Bisc91a]; [Dixo91a]; [Jued91a].",
   COMMENT   = "Was [Chri90a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Chri92b,
   AUTHOR    = "Christianson, D. Bruce",
   TITLE     = "Reverse Accumulation and Attractive Fixed Points",
   TYPE      = "Technical Report",
   NUMBER    = "NOC TR 258",
   INSTITUTION = "The Numerical Optimisation Centre, 
               University of Hertfordshire",
   ADDRESS   = "Hatfield, UK",
   MONTH     = "March",
   YEAR      = "1992",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Civa65a,
   AUTHOR    = "Civalleri, P. P. ", 
   TITLE     = "Cohn's Generalized Theorem", 
   JOURNAL   = "Alta Frequenza",
   YEAR      = "1965",
   VOLUME    = "35",
   NUMBER    = "",
   PAGES     = "797--806",
   MONTH     = "",
   NOTE      = "",
   REFERRED  = "[Irim91a]",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}
 
@BOOK
{
   Clar83a,
   AUTHOR    = "Clark, Frank H",
   TITLE     = "Optimization and Nonsmooth Analysis",
   PUBLISHER = "John Wiley and Sons",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1983",
   REFERRED  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Cole84a,
   AUTHOR    = "Coleman, T. F. 
                and Garbow, B. S. 
                and Mor\'{e}, J. J.",
   TITLE     = "Software for estimating sparse {J}acobian matrices",
   JOURNAL   = "ACM Trans. Math. Software",
   YEAR      = "1984",
   VOLUME    = "10",
   NUMBER    = "",
   PAGES     = "329--345",
   MONTH     = "",
   NOTE      = "",
   REFERRED  = "[Bisc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Cole83a,
   AUTHOR    = "Coleman, T. F. 
                and Mor\'{e}, J. J.",
   TITLE     = "Estimation of sparse {J}acobian
                matrices and graph coloring problems",
   JOURNAL   = "SIAM J. on Numerical Analysis",
   YEAR      = "1984",
   VOLUME    = "20",
   NUMBER    = "",
   PAGES     = "187--209",
   MONTH     = "",
   NOTE      = "",
   REFERRED  = "[Bisc91a]; [Grie91a].",
   COMMENT   = "Griewank gives pages as 368--375.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Cont80a,
   AUTHOR    = "S.~D. Conte 
                and Carl {de~Boor}",
   TITLE     = "Elementary Numerical Analysis",
   PUBLISHER = "McGraw-Hill",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1980",
   REFERRED  = "[Berz91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Cook88a,
   author    = "{Cook, Jr.}, Grant O.",
   title     = "{ALPAL}, a Tool for the Development of Large-scale 
                Simulation Codes",
   institution = "Lawrence Livermore National Laboratory",
   TYPE      = "Technical Report",
   ADDRESS   = " Berkeley, Calif.",
   month     = "August",
   year      = "1988",
   number    = "UCID-21482",
   REFERRED  = "[Char91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Corl87b,
   AUTHOR    = "Corliss, George F.",
   TITLE     = "Performance of self-validating quadrature",
   BOOKTITLE = "Proceedings of the NATO Advanced Workshop on Numerical
                Integration: Recent Developments, Software, and Applications",
   EDITOR    = "Keast, Pat
                and Fairweather, Graeme",
   PUBLISHER = "Reidel",
   ADDRESS   = "Boston",
   YEAR      = "1987",
   PAGES     = "239--259",
   REFERRED  = "Zbl. Math 615 -- 65018; [Corl88a]; [Corl91a].",
   COMMENT   = "quadrature for integral iteration.",
   KEYWORDS  = "interval quadrature; automatic differentiation.",
   ABSTRACT  = "The interval implementation of Gaussian quadrature described
                in [Corl87a] required about 3 - 5 times as long to compute a
                guaranteed bound the $ \int_a^b f(x)\,dx $ as QUADPACK
                required to compute an estimate.",
}


@INCOLLECTION
{
   Corl88a,
   AUTHOR    = "Corliss, George F.",
   TITLE     = "Applications of Differentiation Arithmetic",
   BOOKTITLE = "Reliability in Computing",
   PUBLISHER = "Academic Press",
   EDITOR    = "Moore, Ramon E.",
   ADDRESS   = "London",
   YEAR      = "1988",
   PAGES     = "127--148",
   REFERRED  = "[Layn91a].",
   COMMENT   = "Summary of the work performed by the author in the field of
                differentiation arithmetic.",
   KEYWORDS  = "point algorithms; interval algorithms; differentiation
                arithmetic; preprocessor; quadrature; Taylor series.",
   ABSTRACT  = "This is a discussion of various issues involved in
                differentiation arithmetic.  The use in both point and interval
                algorithms is discussed.  Differentiation arithmetic is
                implemented using the recursion relations for Taylor
                coefficients, or by using a parser to create a Fortran
                subroutine which evaluates the derivatives using
                differentiation arithmetic.  Applications to quadrature and to
                Taylor series solutions of ordinary differential equations is
                discussed."
}


@INCOLLECTION
{
   Corl91a,
   AUTHOR    = "Corliss, George F.",
   TITLE     = "Overloading Point and Interval {T}aylor Operators",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "139--146",
   REFERRED  = "[Jued91a]; [Kalm91a]; [Layn91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Corl91d,
   AUTHOR    = "Corliss, George F.",
   TITLE     = "Automatic Differentiation Bibliography",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "331--353",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Corl82a,
   AUTHOR    = "Corliss, George F.
                and Chang, Y. F.",
   TITLE     = "Solving Ordinary Differential Equations Using {T}aylor Series",
   JOURNAL   = "ACM Trans. Math. Software",
   VOLUME    = "8",
   NUMBER    = "2",
   PUBLISHER = "",
   YEAR      = "1982",
   PAGES     = "114--144",
   REFERRED  = "MR 83g 65072; [Aber88a]; [Chan86a];
                [Corl88a]; [Gupt85a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; Taylor series;
                radius of convergence; pre-processing;
                automatic differentiation.",
   ABSTRACT  = "A Fortran pre-processor program uses automatic differentiation
                to write a Fortran object program which is then run to solve
                the system.  Parts: \begin{enumerate} \item Expand the series
                using recurrence relations. \item Estimate the radius of
                convergence of each component. \item Select a step size by
                comparison with series for model problems. \item Extend the
                solution by analytic continuation.\end{enumerate} The series
                analysis provides valuable information about analytic
                properties of the solution like the location and order of
                primary singularities.  Taylor series methods are shown to be
                competitive with DVERK and DGEAR in terms of speed and accuracy.",
}


@TECHREPORT
{
   Corl88b,
   AUTHOR    = "Corliss, George F.
                and Davis, Paul H
                and Krenz, Gary S.",
   TITLE     = "Bibliography on Interval Methods for the Solution of Ordinary
                Differential Equations",
   TYPE      = "Technical Report",
   NUMBER    = "No. 289",
   INSTITUTION = "Department of Mathematics, Statistics and Computer Science,
                Marquette University",
   ADDRESS   = "Milwaukee, Wisc.",
   MONTH     = "September",
   YEAR      = "1988",
   REFERRED  = "[Davi88b].",
   COMMENT   = "Contains some intersection with this report.  Extension of
                [Corl87c].",
   KEYWORDS  = "bibliography.",
   ABSTRACT  = "This is a bibliography of literature judged by the authors to
                be relevant to interval mathods for the numerical solution of
                initial value problems in ordinary differential equations.  It
                includes citations from the following topics: \begin{itemize}
                \item Interval methods for initial value problems, \item
                Interval methods for boundary value problems, \item Point
                Taylor series methods, \item Point defect correction methods,
                \item Point methods based on Picard iteration, \item Error
                {\em estimation\/} for stiff equations, \item Global error
                {\em estimation,} \item Differentiation arithmetic, and \item
                Interval integration.\end{itemize}",
}


@MISC
{
   Corl91c,
   AUTHOR    = "Corless, Robert M.
                and Corliss, George F.",
   TITLE     = "Automatic Differentiation in Validated Defect Control
                for Ordinary Differential Equations",
   HOWPUBLISHED = "Poster presented at {SIAM} {W}orkshop on
                {A}utomatic {D}ifferentiation of {A}lgorithms, 
                {B}reckenridge, Colo.",
   MONTH     = "January",
   YEAR      = "1991",
   REFERRED  = "",
   COMMENT   = "Submitted to {\sl {IMA} {J}ournal of {N}umerical
                {A}nalysis\/}",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Corl92a,
   AUTHOR = "George Corliss
             and Andreas Griewank
             and Tom Robey
             and Steve Wright",
   TITLE  = "Automatic Differentiation Applied to Unsaturated Flow
             --- {ADOL--C} Case Study",
   INSTITUTION = "Mathematics and Computer Science Division,
             Argonne National Laboratory",
   MONTH     = "April",
   YEAR      = "1992",
   TYPE      = "Technical Memorandum",
   NUMBER    = "ANL/MCS--TM--162",
   ADDRESS   = "Argonne, Ill.",
   NOTE      = "",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Corl87a,
   AUTHOR     = "Corliss, George F.
                 and Rall, Louis B.",
   TITLE      = "Adaptive, Self-Validating Quadrature",
   JOURNAL    = "SIAM J. Sci. Stat. Comput.",
   VOLUME     = "8",
   NUMBER     = "5",
   YEAR       = "1987",
   PAGES      = "831--847",
   REFERRED  = "[Garl85a] \# 311; [Garl87a] \# 311; [Corl88a]; [Jued91a]; 
                [Rall91a].",
   COMMENT   = "Also {\sl MRC Technical Summary Report No. 2815,\/}
                University of Wisconsin-Madison, 1985.",
   KEYWORDS  = "quadrature; automatic differentiation.",
   ABSTRACT  = "Validated bounds for $ If = \int_a^b f(x)\,dx $ are computed
                using Gaussian, Newton-Cotes, or Taylor polynomial quadrature.
                The algorithm uses both subinterval and order adaptation.
                Results often differ by a few units in the last place."
}


@INCOLLECTION
{
   Corl84a,
   AUTHOR    = "Corliss, George F.
                and Rall, Louis B.",
   TITLE     = "Automatic generation of {T}aylor series in {P}ascal-{SC}: 
                {B}asic operations and applications to differential equations",
   BOOKTITLE = "Trans. of the First Army Conference on Applied Mathematics
                and Computing (Washington, D.C., 1983)",
   PUBLISHER = "ARO Rep. 84-1, U. S. Army Res. Office",
   ADDRESS   = "Research Triangle Park, N.C.",
   YEAR      = "1984",
   PAGES     = "177--209",
   REFERRED  = "CMP 741 340; [Garl85a] \# 310; [Garl87a]
                \# 310; [Corl88a]; [Fisc87e]; [Jued91a]; 
                [Rall87a].",
   COMMENT   = "Also appeared as {\sl MRC Technical Summary Report No.2497,\/}
                Mathematics Research Center, University of
                Wisconsin-Madison, 1983.",
   KEYWORDS  = "automatic differentiation; Taylor series; stability.",
   ABSTRACT  = "Pascal-SC supports user-defined data types, user-defined
                operators, and accurate floating point and interval arithmetic
                for numerical computations.  The authors implement data types
                TAYLOR and ITAYLOR (Interval Taylor) with operators $ + $,
                $ - $, $ * $, $ / $, $ ** $, and the functions SQR, SQRT, EXP,
                SIN, COS, ARCTAN, and LN.  An initial value problem
                $ y' = y^2 $, $ y(0) = 1 $, is solved with TAYLOR and with
                ITAYLOR types to show that the series generation exhibits a
                mild instability which has no significant effect on the values
                of the solution computed by analytic continuation."
}


@INCOLLECTION
{
   Corl91b,
   AUTHOR    = "Corliss, George F.
                and Rall, Louis B.",
   TITLE     = "Computing the Range of Derivatives",
   BOOKTITLE = "Computer Arithmetic, Scientific Computation, and Mathematical
                Modelling",
   YEAR      = "1991",
   PAGES     = "195--212",
   PUBLISHER = "J. C. Baltzer AG",
   ADDRESS   = "Basel",
   SERIES    = "{IMACS} Annals on Computing and Applied Mathematics",
   VOLUME    = "12",
   EDITOR    = "Kaucher, Edgar
                and Markov, S. M.
                and Mayer, Gunter",
   NOTE      = "",
   REFERRED  = "[Corl91a]; [Jued91a]; [Rall91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Cour85a,
   AUTHOR    = "Courtier, P.",
   TITLE     = "Experiments in Data Assimilation Using the Adjoint 
                Model Technique",
   BOOKTITLE = "Proceedings of the Workshop on High-Resolution 
                Analysis ECMWF (UK)",
   PUBLISHER = "",
   MONTH     = "June",
   YEAR      = "1985",
   PAGES     = "",
   REFERRED  = "[Navo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Cour87b,
   AUTHOR    = "Courtier, P.",
   TITLE     = "Application of Optimal Control to Numerical 
                Meteorological Forecasting",
   TYPE      = "{D}octoral thesis",
   INSTITUTION = "Universit\'{e} Pierre-et-Marie-Curie",
   ADDRESS   = "Paris, France",
   MONTH     = "",
   YEAR      = "1987",
   REFERRED  = "[Tala91a].",
   NOTE      = "(In French).",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Cour87a,
   AUTHOR    = "Courtier, P.
                and Talagrand, Olivier",
   TITLE     = "Variational Assimilation of Meteorological 
                Observations with the Adjoint 
                Equation -- {P}art {II}. {N}umerical Results",
   JOURNAL   = "Q. J. R. Meteorol. Soc.",
   VOLUME    = "113",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1987",
   PAGES     = "1329--1347",
   REFERRED  = "[Navo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Cour90a,
   AUTHOR    = "Courtier, P.
                and Talagrand, Olivier",
   TITLE     = "Variational Assimilation of Meteorological 
                Observations with the Direct and Adjoint Shallow-Water 
                Equations",
   JOURNAL   = "Tellus",
   VOLUME    = "42A",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1990",
   PAGES     = "531--549",
   REFERRED  = "[Tala91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Cour90b,
   AUTHOR    = "Courtier, P.
                and Thepaut, J. N.
                and Talagrand, Olivier",
   TITLE     = "4-dimensional data assimilation using the adjoint 
                of a primitive equation model",
   BOOKTITLE = "Proceedings of the International Symposium on Assimilation 
                of Observations in Meteorology and Oceanography, World 
                Meteorological Organization, Geneva, Switzerland",
   PUBLISHER = "",
   YEAR      = "1990",
   PAGES     = "337--340",
   REFERRED  = "[Tala91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Crar75a,
   AUTHOR    = "Crary, F. D.",
   TITLE     = "The {AUGMENT} precompiler.  {II}. {T}echnical documentation",
   TYPE      = "MRC Technical Summary Report",
   NUMBER    = "No. 1470",
   INSTITUTION = "Mathematics Research Center, 
                University of Wisconsin-Madison",
   YEAR      = "1975",
   REFERRED  = "[Corl91a]; [Crar79a]; [Rall80a].",
   COMMENT   = "AUGMENT is important as a possible vehicle for the
                implementation of differentiation arithmetic and/or interval
                arithmetic.",
   KEYWORDS  = "precompiler.",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Crar76a,
   AUTHOR    = "Crary, F. D.",
   TITLE     = "The {AUGMENT} precompiler.  {I}. {U}ser information",
   TYPE      = "MRC Technical Summary Report",
   NUMBER    = "No. 1469",
   INSTITUTION = "Mathematics Research Center, 
                University of Wisconsin-Madison",
   YEAR      = "1976",
   PAGES     = "",
   REFERRED  = "[Crar79a]; [Rall80a].",
   COMMENT   = "AUGMENT is important as a possible vehicle for the
                implementation of differentiation arithmetic and/or interval
                arithmetic.",
   KEYWORDS  = "precompiler.",
   ABSTRACT  = ""
}


@ARTICLE
{
   Crar79a,
   AUTHOR    = "Crary, F. D.",
   TITLE     = "A versatile precompiler for nonstandard arithmetics",
   JOURNAL   = "ACM Trans. Math. Software",
   YEAR      = "1979",
   VOLUME    = "5",
   NUMBER    = "2",
   PAGES     = "204--217",
   REFERRED  = "[Corl87a]; [Corl88a]; [Yohe79a].",
   COMMENT   = "",
   KEYWORDS  = "precompiler; nonstandard arithmetics.",
   ABSTRACT  = "A highly portable Fortran precompiler which allows simplified
                computation with nonstandard arithmetics is described.  The
                philosophy and design goals are briefly presented, the major
                capabilities of the precompiler are described, and some
                applications are discussed.  A summary is made of experience
                with the precompiler.  The author's aim is to furnish
                programmers with a ready means of using nonstandard arithmetics."
}

@ARTICLE
{
   Datt91a,
   AUTHOR    = "Datta, S.
                and Nugent, J.
                and Tishler, A.
                and Wang, J. L.",
   TITLE     = "Seasonality, Differential Access, and Interlinking
                of Labour and Credit",
   JOURNAL   = "J. Development Studies",
   YEAR      = "to appear",
   VOLUME    = "",
   NUMBER    = "",
   PAGES     = "",
   REFERRED  = "[Tesf91a]"
}


@BOOK
{
   Davi81a,
   AUTHOR    = "Davie, A. J. T.
                and Morrison, R.",
   TITLE     = "Recursive Descent Compiling",
   PUBLISHER = "Ellis-Horwood",
   SERIES    = "",
   ADDRESS   = "Chichester",
   YEAR      = "1981",
   REFERRED  = "[Garc91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Davi88a,
   AUTHOR    = "Davis, Paul H.
                and Corliss, George F.
                and Krenz, Gary S.",
   TITLE     = "A Bibliography on Methods and Techniques in Differentiation
                Arithmetic",
   TYPE      = "Technical Report",
   NUMBER    = "{AM}--88--09",
   INSTITUTION = "School of Mathematics, University of Bristol",
   ADDRESS   = "Bristol, U.K.",
   YEAR      = "1988",
   REFERRED  = "[Corl91a]; [Davi88b].",
   COMMENT   = "Basis for this bibliography.",
   KEYWORDS  = "differentiation arithmetic, bibliography.",
   ABSTRACT  = "The authors gather together all references known to them
                relating to methods, techniques, algorithms, or applications
                of differentiation arithmetic."
}


@TECHREPORT
{
   Davi87a,
   AUTHOR    = "Davis, Paul H.
                and Pryce, John D.",
   TITLE     = "A New Implementation of Automatic Differentiation for Use
                with Numerical Software",
   TYPE      = "Technical Report",
   NUMBER    = "AM--87--11",
   INSTITUTION = "School of Mathematics, University of Bristol",
   ADDRESS   = "Bristol, U.K.",
   YEAR      = "1987",
   PAGES     = "",
   REFERRED  = "[Step87a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; differentiation arithmetic; parser.",
   ABSTRACT  = "A sparse automatic differentiation technique for calculating
                partial derivatives is presented.  The algorithms only
                calculate the derivatives of a function which are not
                identically zero.  The algorithms derived can be used to
                calculate the derivatives of a function to an arbitrary
                level.  It is shown how to implement the technique in a
                numerical software package using a parsing technique."
}


@INCOLLECTION
{
   Davi92a,
   AUTHOR    = "Davis, Paul H.
                and Pryce, John D.
                and Stephens, Bruce",
   TITLE     = "Recent Developments in Automatic Differentiation",
   BOOKTITLE = "Scientific Software Systems",
   YEAR      = "1990",
   EDITOR    = "J. C. Mason
                and M. G. Cox",
   PUBLISHER = "Chapman and Hall",
   ADDRESS   = "11 New Fetter Lane, London EC4P 4EE",
   PAGES     = "153--165",
   NOTE      = "Also appeared as Technical Report ACM--89--1,
                Royal Military College of Science at Shrivenham,
                Shrivenham, U.K.",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Davi88b,
   AUTHOR    = "Davis, Paul H.
                and Stephens, Bruce
                and Corliss, George F.
                and Krenz, Gary S.",
   TITLE     = "Specification of a Preprocessor for Use with
                Differentiation Arithmetic",
   TYPE      = "Technical Report",
   NUMBER    = "AM--88--08",
   INSTITUTION = "School of Mathematics, University of Bristol",
   ADDRESS   = "Bristol, U.K.",
   YEAR      = "1988",
   MONTH     = "September",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "differentiation arithmetic, coder.",
   ABSTRACT  = "This report documents discussions held by the authors on the
               specification and design of a general purpose computer
               package to support differentiation arithmetic.  They
               consider the rationale and applications of differentiation
               arithmetic, outline the general structure of a
               coder-operators system, and describe the specifications for
               the coder, the operators, and their interface."
}


@ARTICLE
{
   Denn81a,
   AUTHOR    = "Dennis, John
                and Gay, David
                and Welsch, R. E.",
   TITLE     = "Algorithm 573. {NL2SOL} --- {A}n Adaptive Nonlinear 
                Least-Squares Algorithm",
   JOURNAL   = "ACM Trans. Math. Software",
   VOLUME    = "7",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1981",
   PAGES     = "369--383",
   REFERRED  = "[Gayd91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Denn83a,
   AUTHOR    = "Dennis, John
                and Schnabel, Robert B.",
   TITLE     = "Numerical Methods for Unconstrained
                Optimization and Nonlinear Equations",
   PUBLISHER = "Prentice-Hall",
   YEAR      = "1983",
   VOLUME    = "",
   SERIES    = "",
   ADDRESS   = "Englewood Cliffs, N.J.",
   EDITION   = "",
   MONTH     = "",
   REFERRED  = "[Bisc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}
 

@PHDTHESIS
{
   Derb85a,
   AUTHOR    = "Derber, J. C.",
   TITLE     = "The Variational 4-D Assimilation of Analyses Using 
                Filtered Models as Constraints",
   SCHOOL    = "University of Wisconsin-Madison",
   ADDRESS   = "Madison, Wisc.",
   MONTH     = "",
   YEAR      = "1985",
   REFERRED  = "[Navo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Dewa89a,
   author    = "M. C. Dewar",
   title     = "{IRENA} --- {A}n integrated symbolic and numerical 
                computational environment",
   booktitle = "Proceedings of the 1989 International Symposium 
                on Symbolic and Algebraic Computation",
   year      = "1989",
   editor    = "Gaston H. Gonnet",
   pages     = "171--179",
   REFERRED  = "[Char91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Dewa90a,
   author    = "M. C. Dewar 
                and M. G. Richardson",
   title     = "Reconciling Symbolic and Numeric Computation in 
                a Practical Setting",
   booktitle = "Design and Implementation of Symbolic Computing 
                Systems, Proceedings of DISCO 90",
   year      = "1990",
   editor    = "A. Miola",
   pages     = "195--204",
   publisher = "Springer Verlag",
   ADDRESS   = "Berlin",
   month     = "April",
   SERIES    = "Lecture Notes in Computer Science",
   VOLUME    = "429",
   note      = "",
   REFERRED  = "[Char91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}
 

@TECHREPORT
{
   LeDi82a,
   AUTHOR    = "F.-X. {Le Dimet}",
   TITLE     = "A General Formalism of Variational Analysis",
   INSTITUTION = "CIMMS",
   MONTH     = "",
   YEAR      = "1982",
   TYPE      = "Report",
   NUMBER    = "No. 22",
   ADDRESS   = "Norman, Okla.",
   REFERRED  = "[Navo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   LeDi86b,
   AUTHOR    = "F.-X. {Le Dimet} 
                and A. Nouailler",
   TITLE     = "Assimilation of Dynamic Data in a Limited-Area Model",
   BOOKTITLE = "Variational Methods in Geosciences",
   YEAR      = "1986",
   EDITOR    = "Sasaki, Y. K.",
   PUBLISHER = "Elsevier",
   ADDRESS   = "Amsterdam",
   PAGES     = "181--198",
   REFERRED  = "[Navo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   LeDi86a,
   AUTHOR    = "F.-X. {Le Dimet} 
                and O. Talagrand",
   TITLE     = "Variational algorithms for analysis and 
                assimilation of meteorological observations:  
                {T}heoretical aspects",
   JOURNAL   = "Tellus",
   VOLUME    = "38A",
   NUMBER    = "",
   YEAR      = "1986",
   PAGES     = "97--110",
   REFERRED  = "[Thac91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Dixo87a,
   AUTHOR    = "Dixon, Lawrence C. W.",
   TITLE     = "Automatic Differentiation and Parallel Processing in
                Optimisation",
   TYPE      = "Technical Report",
   NUMBER    = "No. 180",
   INSTITUTION = "The Numerical Optimisation Center, Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   YEAR      = "1987",
   REFERRED  = "[Bisc91a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; numerical results; differentiation arithmetic.
                optimisation method.",
   ABSTRACT  = "The concepts of automatic differentiation, see [Rall81a], and
                of parallel processing are applied to problems in optimisation.
                A discussion is presented of how the advent of the Ada
                programming language on parallel processing machines may
                transform the solution of practical optimisation problems, see
                [Dixo87b].  The author also discusses the difficulties
                associated with calculating the derivative values if automatic
                differentiation is not used.",
}


@INCOLLECTION
{
   Dixo91a,
   AUTHOR    = "Dixon, Lawrence C. W.",
   TITLE     = "Use of Automatic Differentiation for Calculating
                {H}essians and {N}ewton Steps",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "114--125",
   REFERRED  = "[Grie91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Dixo87b,
   AUTHOR    = "Dixon, Lawrence C. W.
                and Mohseninia, M.",
   TITLE     = "The Use of the Extended Operations Set of {ADA} with Automatic
                Differentiation and the Truncated {N}ewton Method",
   TYPE      = "Technical Report",
   NUMBER    = "No. 176",
   INSTITUTION = "The Numerical Optimisation Center, Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   YEAR      = "1987",
   PAGES     = "",
   REFERRED  = "[Dixo87a]; [Dixo89b]; [Pric87a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; differentiation arithmetic; optimisation.",
   ABSTRACT  = "It is shown how the extended operations set of Ada can be
                used to allow automatic differentiation to be specified in a
                natural way.  This is then applied to solving optimisation
                problems using the truncated Newton method, see [Dixo86a]."
}



@TECHREPORT
{
   Dixo87c,
   AUTHOR    = "Dixon, Lawrence C. W.
                and Maany, Z.",
   TITLE     = "The Echelon Method for the Solution of Sparse Sets of
                Linear Equations",
   TYPE      = "Technical Report",
   NUMBER    = "NOC TR177",
   INSTITUTION = "The Numerical Optimisation Center, Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   MONTH     = "February",
   YEAR      = "1988",
   PAGES     = "",
   REFERRED  = "[Dixo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Dixo89b,
   AUTHOR    = "Dixon, Lawrence C. W.
                and Maany, Z.",
   TITLE     = "The Performance of the Truncated {N}ewton, Conjugate Gradient
                Algorithm in {F}ortran and {A}da",
   TYPE      = "Technical Report",
   NUMBER    = "NOC TR210",
   INSTITUTION = "The Numerical Optimisation Center, Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   MONTH     = "June",
   YEAR      = "1989",
   PAGES     = "",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "optimization",
   ABSTRACT  = "We compare the performance of Fortran and Ada implementations
                of the truncated Newton, conjugate gradient approach for
                solving unconstrained optimization problems.  Automatic
                differentiation is used to calculate first and second
                derivatives in both Fortran and Ada -- Authors' abstract.",
}


@TECHREPORT
{
   Dixo88b,
   AUTHOR    = "Dixon, Lawrence C. W.
                and Maany, Z.
                and Mohseninia, M.",
   TITLE     = "Finite Element Optimization in {A}da Using Automatic 
                Differentiation",
   TYPE      = "Technical Report",
   NUMBER    = "NOC TR205",
   INSTITUTION = "The Numerical Optimisation Center, Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   MONTH     = "",
   YEAR      = "1988",
   PAGES     = "",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; differentiation arithmetic; optimisation.",
   ABSTRACT  = "It is shown how the extended operations set of Ada can be
                used to allow automatic differentiation to be specified in a
                natural way.  This is then applied to solving optimisation
                problems using the truncated Newton method, see [Dixo86a].",
}


@ARTICLE
{
   Dixo90a,
   AUTHOR    = "Dixon, Lawrence C. W.
                and Maany, Z.
                and Mohseninia, M.",
   TITLE     = "Automatic Differentiation of Large Sparse Systems",
   JOURNAL   = "J. Economic Dynamics \& Control",
   VOLUME    = "14",
   NUMBER    = "2",
   YEAR      = "1990",
   PAGES     = "",
   REFERRED  = "[Dixo91a].",
   NOTE      = "Presented at IFAC on Dynamic Modelling \& Control of 
                National Economies, Edinburgh, July, 1989.
                Also appeared as Technical Report NOC TR223,
                The Numerical Optimisation Center, Hatfield Polytechnic,
                Hatfield, U.K., July 1989.",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Dixo87d,
   AUTHOR    = "Dixon, Lawrence C. W.
                and Mohseninia, M.",
   TITLE     = "The Use of the Extended Operations Set of {A}da with Automatic
                Differentiation and the Truncated {N}ewton Method",
   TYPE      = "Technical Report",
   NUMBER    = "NOC TR176",
   INSTITUTION = "The Numerical Optimisation Center, Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   MONTH     = "April",
   YEAR      = "1987",
   REFERRED  = "[Dixo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Dixo86a,
   AUTHOR    = "Dixon, Lawrence C. W.
                and Price, Richard C.",
   TITLE     = "The Truncated {G}auss-{N}ewton Method for Sparse Least Squares
                Problems Using Automatic Differentiation",
   TYPE      = "Technical Report",
   NUMBER    = "No. 171",
   INSTITUTION = "The Numerical Optimisation Center, Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   YEAR      = "1986",
   REFERRED  = "[Dixo87a]; [Fisc87e].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; numerical results; differentiation arithmetic;
                optimisation method.",
   ABSTRACT  = "The automatic differentiation technique described in [Dixo86a]
                is applied to the solution of least squares problems using a
                truncated Gauss-Newton method.  The method is tested on eight
                standard test problems."
}


@TECHREPORT
{
   Dixo86c,
   AUTHOR    = "Dixon, Lawrence C. W.
                and Dolan, P.
                and Price, Richard C.",
   TITLE     = "Finite Element Optimisation: {T}he Use of Structured Automatic
                Differentiation",
   TYPE      = "Technical Report",
   NUMBER    = "No. 175",
   INSTITUTION = "The Numerical Optimisation Center, Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   YEAR      = "1986",
   REFERRED  = "[Fisc87e].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; numerical results; differentiation arithmetic;
                optimisation method.",
   ABSTRACT  = "A finite element optimisation algorithm is presented which uses
                the technique of automatic differentiation described in
                [Dixo86a].  The method is illustrated by reference to two
                dimensional flow problems that have been implemented on the
                ICL (AMT) DAP parallel processing computer."
}


@TECHREPORT
{
   Dixo86b,
   AUTHOR    = "Dixon, Lawrence C. W.
                and Price, Richard C.",
   TITLE     = "The Truncated {N}ewton Method for Sparse Unconstrained
                Optimisation Using Automatic Differentiation",
   TYPE      = "Technical Report",
   NUMBER    = "NOC TR170",
   INSTITUTION = "The Numerical Optimisation Center, Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   MONTH     = "October",
   YEAR      = "1986",
   PAGES     = "",
   REFERRED  = "[Dixo87a]; [Dixo91a]; [Fisc87e].",
   COMMENT   = "This paper was presented at the SIAM National meeting, Boston,
                1986.  Also to appear in J. Opt. Theory and Appl. 60(2),
                pp. 261--275, February 1989.",
   KEYWORDS  = "point algorithm; numerical results; differentiation arithmetic;
                optimisation method.",
   ABSTRACT  = "A method is presented which solves unconstrained optimisation
                problems using a truncated Newton method.  Automatic
                differentiation is used to calculate the derivatives
                required.  By taking advantage of the structure of the
                optimisation method, only vector storage is required since the
                Hessian is multiplied by a vector during the computation of
                the derivatives.  Numerical results obtained by solving
                standard test problems are presented.",
}


@ARTICLE
{
   Dixo89a,
   AUTHOR    = "Dixon, Lawrence C. W.
                and Price, Richard C.",
   TITLE     = "The Truncated {N}ewton Method for Sparse Unconstrained
                Optimisation Using Automatic Differentiation",
   JOURNAL   = "J. Opt. Theory and Appl.",
   VOLUME    = "60",
   NUMBER    = "2",
   MONTH     = "February",
   YEAR      = "1989",
   PAGES     = "261 +",
   REFERRED  = "[Dixo91a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; numerical results; differentiation arithmetic;
                optimisation method.",
   ABSTRACT  = "A method is presented which solves unconstrained optimisation
                problems using a truncated Newton method.  Automatic
                differentiation is used to calculate the derivatives
                required.  By taking advantage of the structure of the
                optimisation method, only vector storage is required since the
                Hessian is multiplied by a vector during the computation of
                the derivatives.  Numerical results obtained by solving
                standard test problems are presented."
}


@ARTICLE
{
   Dixo88a,
   AUTHOR    = "Dixon, L. C. W.
                and Price, Richard C.",
   TITLE     = "Numerical experience with the truncated {N}ewton method",
   JOURNAL   = "J. Opt. Theory and Appl.",
   VOLUME    = "56",
   NUMBER    = "2",
   YEAR      = "1988",
   PAGES     = "245--255",
   REFERRED  = "[Dixo87a].",
   COMMENT   = "Also appeared in {\sl Technical Report No. 169\/,} The
                Numerical Optimisation Center, Hatfield Polytechnic, Hatfield,
                UK (1986).",
   KEYWORDS  = "point algorithm; numerical results; optimisation method.",
   ABSTRACT  = "The truncated Newton method is presented for use with large
                sparse unconstrained optimisation problems.  It is tested on
                four problems under various conditions."
}


@ARTICLE
{
   Drey69a,
   AUTHOR    = "Dreyfus, S. E.",
   TITLE     = "An appraisal of some shortest path algorithms",
   JOURNAL   = "Operations Research",
   VOLUME    = "17",
   NUMBER    = "",
   YEAR      = "1969",
   PAGES     = "395--412",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Dole90a,
   AUTHOR    = "Doleh, Y.
                and Wang, P. S.",
   TITLE     = "{SUI}: {A} system independent user interface for an 
                integrated scientific computing environment",
   BOOKTITLE = "Proceedings ISSAC '90",
   YEAR      = "1990",
   EDITOR    = "Watanabe, S.
                and Nagata, M.",
   PUBLISHER = "ACM Press",
   ADDRESS   = "New York",
   PAGES     = "88--95",
   REFERRED  = "[Gold91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Doua90a,
   AUTHOR    = "Douady, D.
                and Talagrand, Olivier",
   TITLE     = "The impact of threshold processes on variational assimilation",
   BOOKTITLE = "Proceedings of the International Symposium on Assimilation
                of Observations in Meteorology and Oceanography, World
                Meteorological Organization, Geneva, Switzerland",
   PUBLISHER = "",
   YEAR      = "1990",
   PAGES     = "486--487",
   REFERRED  = "[Tala91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Duff87a,
   AUTHOR    = "Duff, I. S. 
                and Anoli, M. 
                and Gould, N. I. M.
                and Reid, J. K.",
   TITLE     = "The Practical Use of the {H}ellerman-{R}anck P$^4$ 
                Algorithm and the P$^5$ Algorithm of {E}risman et al.",
   INSTITUTION = "AERE Harwell",
   MONTH     = "",
   YEAR      = "1987",
   TYPE      = "Report",
   NUMBER    = "CSS213",
   ADDRESS   = "",
   REFERRED  = "[Dixo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Duff86a,
   AUTHOR    = "I. S. Duff
                and A. M. Erisman 
                and J. K. Reid",
   TITLE     = "Direct Methods for Sparse Matrices",
   PUBLISHER = "Clarendon Press",
   SERIES    = "Oxford Science Publications",
   ADDRESS   = "Oxford",
   YEAR      = "1986",
   REFERRED  = "[Grie91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Duff74a,
   AUTHOR    = "Duffin, R.",
   TITLE     = "On {F}ourier's analysis of linear inequality systems",
   JOURNAL   = "Mathematical Programming Study",
   VOLUME    = "1",
   NUMBER    = "",
   YEAR      = "1974",
   PAGES     = "71--95",
   REFERRED  = "[Saar91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Eise68a,
   author    = "Harry Eisenpress 
                and Abel Bomberault",
   title     = "Efficient Symbolic Differentiation using {PL/I-F}ormac",
   TYPE      = "Technical Report",
   institution = "IBM New York Scientific Research Center",
   ADDRESS   = "Yorktown Heights, N.Y.",
   year      = "1968",
   number    = "320--2956",
   month     = "September",
   REFERRED  = "[Char91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Engq80a,
   author    = "Bjorn Engquist 
                and Tom Smedsaas",
   title     = "Automatic computer code generation for hyperbolic and
                parabolic differential equations",
   JOURNAL    = "SIAM J. Sci. Stat. Comput.",
   year      = "1980",
   volume    = "1",
   number    = "2",
   pages     = "249--259",
   month     = "June",
   REFERRED  = "[Char91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Elli90a,
   AUTHOR    = "Margaret~A. Ellis 
                and Bjarne Stroustrup",
   TITLE     = "The Annotated {C}++ Reference Manual",
   PUBLISHER = "Addison-Wesley",
   SERIES    = "",
   ADDRESS   = "Reading, Mass.",
   YEAR      = "1990",
   REFERRED  = "[Kalm91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Enri87a,
   AUTHOR    = "Enright, Wayne H.
                and Pryce, John D.",
   TITLE     = "Two {FORTRAN} Packages for Assessing Initial Value Methods",
   JOURNAL   = "ACM Trans. Math. Software",
   VOLUME    = "13",
   NUMBER    = "1",
   YEAR      = "1987",
   PAGES     = "1--22",
   REFERRED  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Esco76a,
   AUTHOR    = "Escobal, P. R.",
   TITLE     = "Methods of Orbit Determination",
   EDITION   = "2nd",
   PUBLISHER = "Robert E. Krieger Publishing",
   SERIES    = "",
   ADDRESS   = "",
   YEAR      = "1976",
   REFERRED  = "[Layn91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Evtu85a,
   AUTHOR    = "Evtushenko, {\Yu}ri G.",
   TITLE     = "Numerical Optimization Techniques",
   PUBLISHER = "Optimization Software Inc.",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1985",
   REFERRED  = "[Evtu91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Evtu91a,
   AUTHOR    = "Evtushenko, {\Yu}ri G.",
   TITLE     = "Automatic Differentiation Viewed from Optimal Control",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "25--30",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = ""
}


@BOOK
{
   Evtu89b,
   AUTHOR    = "Evtushenko, {\Yu}ri G.
                and Mazourik, Vladimir P.",
   TITLE     = "Optimization Software",
   PUBLISHER = "Znanie",
   SERIES    = "",
   ADDRESS   = "Moscow",
   YEAR      = "1989",
   REFERRED  = "[Evtu91a].",
   NOTE      = "(In Russian).",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Evtu89a,
   AUTHOR    = "Evtushenko, {\Yu}ri G.
                and Zhadan, V. G.",
   TITLE     = "New approaches in optimization techniques",
   BOOKTITLE = "Proceedings of the 14th IFIP Conference on System 
                Modelling and Optimization",
   YEAR      = "1989",
   EDITOR    = "",
   PUBLISHER = "Springer Verlag",
   SERIES    = "Lecture Notes in Control and Information Science No. 143",
   ADDRESS   = "",
   PAGES     = "23--27",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Fate69a,
   AUTHOR    = "Fateman, Richard J.",
   TITLE     = "Optimal Code for Serial and Parallel Computation",
   JOURNAL   = "Comm. ACM",
   YEAR      = "1969",
   VOLUME    = "12",
   NUMBER    = "12",
   PAGES     = "694--695",
   MONTH     = "December",
   REFERRED  = "[Char91a].",
   COMMENT   = "Discusses Breuer's paper as it relates to symbolic algebra.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Fate74a,
   AUTHOR    = "Fateman, Richard J.",
   TITLE     = "Polynomial Multiplication, Powers, and asymptotic Analysis:
                {S}ome Comments",
   JOURNAL   = "SIAM J. Comput.",
   VOLUME    = "3",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1974",
   PAGES     = "196--213",
   REFERRED  = "[Bren78a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Feld90a,
   AUTHOR    = "S. I. Feldman
                and David  M. Gay 
                and M. W. Maimone 
                and N. L. Schryer",
   TITLE     = "A {F}ortran-to-{C} Converter",
   INSTITUTION = "AT\&T Bell Laboratories",
   ADDRESS   = "Murray Hill, N.J.",
   MONTH     = "",
   YEAR      = "1990",
   TYPE      = "Computing Science Technical Report",
   NUMBER    = "No. 149",
   REFERRED  = "[Gayd91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Feld83a,
   AUTHOR    = "S. I. Feldman
                and P. J. Weinberger",
   TITLE     = "A Portable {F}ortran 77 Compiler",
   BOOKTITLE = "Unix Programmer's Manual, Volume II",
   PUBLISHER = "Holt, Rinehart and Winston",
   SERIES    = "",
   ADDRESS   = "",
   YEAR      = "1983",
   REFERRED  = "[Gayd91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Fiel86a,
   AUTHOR    = "Fields, D. E. 
                and others",
   TITLE     = "{PRESTO-II}:  {A} Low-Level Waste Environment
                Transport and Risk Assessment Code",
   INSTITUTION = "Martin Marietta Energy Systems, Inc., 
                Oak Ridge National Laboratory",
   YEAR      = "1986",
   TYPE      = "",
   NUMBER    = "ORNL-5970",
   ADDRESS   = "Oak Ridge, Tenn.",
   REFERRED  = "[Horw91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@PHDTHESIS
{
   Fisc90b,
   AUTHOR    = "Fischer, Hans-C.",
   TITLE     = "Schnelle Automatische {D}ifferentiation, 
                {E}inschlie{\ss}ungsmethoden und {A}nwendungen",
   SCHOOL    = "Univ. Karlsruhe",
   ADDRESS   = "",
   YEAR      = "1990",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = ""
}


@MISC
{
   Fisc91a,
   AUTHOR    = "Fischer, Hans-C.",
   TITLE     = "Differentiation Arithmetic and Applications in {Pascal-XSC}",
   HOWPUBLISHED = "Poster presented at {SIAM} {W}orkshop on
                {A}utomatic {D}ifferentiation of {A}lgorithms, {B}reckenridge, Colo.",
   MONTH     = "January",
   YEAR      = "1991",
   REFERRED  = "[Corl91a]; [Layn91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Fisc87a,
   AUTHOR    = "Fischer, Herbert",
   TITLE     = "Automatic differentiation: {F}ast method to compute the scalar
               product of gradient and given vector",
   TYPE      = "Technical Report",
   NUMBER    = "No. 105",
   INSTITUTION = "Technische Universt{\"a}t M{\"u}nchen, Institut f{\"u}r
               Angewandte Mathematik und Statistik",
   YEAR      = "1987",
   REFERRED  = "[Fisc87b]; [Fisc87e].",
   COMMENT   = "",
   NOTE      = "Also appeared as Report 26, 
                Schwerpunkt\-programm der Deutschen Forschungsgemeinschaft
                Anwendunsbezogene Optimierung und Steurung, 1987",
   KEYWORDS  = "Differentiation arithmetic.",
   ABSTRACT  = "This method describes a technique of differentiation
               arithmetic which uses as one of the basic operations
               $a+b*c$.  This allows the technique to be faster and use
               less space than the basic method.",
}


@TECHREPORT
{
   Fisc87b,
   AUTHOR    = "Fischer, Herbert",
   TITLE     = "Automatic differentiation: {F}ast method to compute the
               quadratic form of {H}essian matrix and given vector",
   TYPE      = "Technical Report",
   NUMBER    = "No. 108",
   INSTITUTION = "Technische Universt{\"a}t M{\"u}nchen, Institut f{\"u}r
               Angewandte Mathematik und Statistik",
   YEAR      = "1987",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "Differentiation arithmetic.",
   ABSTRACT  = "This method describes a technique of differentiation
               arithmetic which uses as one of the basic operations
               $a+b*c$.  This allows the technique to be faster and use
               less space than the basic method.",
}


@TECHREPORT
{
   Fisc87c,
   AUTHOR    = "Fischer, Herbert",
   TITLE     = "Automatic differentiation: {F}ast method to compute $f''(u)vv$
               for given vector-valued $f$ and given $u$, $v$",
   TYPE      = "Technical Report",
   NUMBER    = "",
   INSTITUTION = "Technische Universt{\"a}t M{\"u}nchen, Institut f{\"u}r
               Angewandte Mathematik und Statistik",
   YEAR      = "1987",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "Differentiation arithmetic.",
   ABSTRACT  = "Consider calculating the function $f''(u)vv$ for a given
               vector-valued f and given u, v, by using the affine function
               $ w: R \rightarrow R^n $ with $w(t) = u + t*v$, and the
               function $\psi: E \subseteq R \rightarrow R^n$ with $\psi(t) =
               f(w(t))$.  Obviously $\psi''(0)11 = f''(u)vv =$ the vector
               wanted.  The paper exploits this fact to produce a fast
               method for computing $f''(u)vv$.  Operation counts are given
               for both the usual method and the fast method.",
}


@ARTICLE
{
   Fisc90a,
   AUTHOR    = "Fischer, Herbert",
   TITLE     = "Automatic differentiation: {P}arallel computation of 
               function, gradient and {H}essian matrix",
   JOURNAL   = "Parallel Computing",
   VOLUME    = "13",
   NUMBER    = "",
   YEAR      = "1990",
   PAGES     = "101--110",
   REFERRED  = "[Bisc91a].",
   COMMENT   = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Fisc87d,
   AUTHOR    = "Fischer, Herbert",
   TITLE     = "Berechnung des {G}radienten mit Automatischen 
                {D}ifferenzieren",
   TYPE      = "Technical Report",
   NUMBER    = "No. 103B",
   INSTITUTION = "Technische Universt{\"a}t M{\"u}nchen, Institut f{\"u}r
               Angewandte Mathematik und Statistik",
   MONTH     = "December",
   YEAR      = "1987",
   REFERRED  = "[Fisc87a]; [Fisc87e].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Fisc87e,
   AUTHOR    = "Fischer, Herbert",
   TITLE     = "Automatic Differentiation:  {H}ow to Compute the {H}essian
                matrix",
   TYPE      = "Report",
   NUMBER    = "No. 26",
   INSTITUTION = "Schwerpunktprogramm der Deutschen Forschungsgemeinschaft
                Anwendunsbezogene Optimierung und Steurung",
   YEAR      = "1987",
   REFERRED  = "[Fisc87e].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Fisc91b,
   AUTHOR    = "Fischer, Herbert",
   TITLE     = "Special Problems in Automatic Differentiation",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "43--50",
   REFERRED  = "[Garc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Fisc91c,
   AUTHOR    = "Fischer, Herbert",
   TITLE     = "Automatic differentiation of the vector that solves 
                a parametric linear system",
   JOURNAL   = "J. Computational and Applied Mathematics",
   VOLUME    = "35",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "to appear",
   PAGES     = "",
   REFERRED  = "[Fisc91b].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@article
{
   Fitc85a,
   author    = "John Fitch",
   title     = "Solving algebraic problems with {REDUCE}",
   journal   = "J. Symbolic Computation",
   pages     = "211--227",
   volume    = "1",
   number    = "2",
   month     = "June",
   year      = "1985",
   REFERRED  = "[Char91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Flaj87a,
   AUTHOR    = "Flajolet, P.
                and Steyaert, J.-M.",
   TITLE     = "A Complexity Calculus for Recursive Tree Algorithms",
   JOURNAL   = "Mathematical Systems Theory",
   VOLUME    = "19",
   NUMBER    = "",
   YEAR      = "1987",
   PAGES     = "301--331",
   REFERRED  = "[Gold91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Flaj90a,
   AUTHOR    = "Flajolet, P.
                and Sipala, P.
                and Steyaert, J.-M.",
   TITLE     = "Analytic Variations on the Common Subexpression Problem",
   INSTITUTION = "INRIA-Rocquencourt",
   YEAR      = "1990",
   TYPE      = "Rapports de Recherche",
   NUMBER    = "1210",
   ADDRESS   = "78153 Le Chesnay Cedex, France",
   REFERRED  = "[Gold91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Flan84a,
   AUTHOR    = "Flanders, Harley",
   TITLE     = "Scientific Pascal",
   PUBLISHER = "Reston Publishing Company",
   SERIES    = "",
   ADDRESS   = "Reston, Virginia",
   YEAR      = "1984",
   REFERRED  = "[Flan91a].",
   COMMENTS  = "Out of print.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Flan91a,
   AUTHOR    = "Flanders, Harley",
   TITLE     = "Automatic Differentiation of Composite Functions",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "95--99",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MISC
{
   Flan91b,
   AUTHOR    = "Flanders, Harley",
   TITLE     = "Response to electronic mail survey",
   HOWPUBLISHED = "Personal communication",
   MONTH     = "March",
   YEAR      = "1991",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Flet65a,
   AUTHOR    = "Fletcher, R.",
   TITLE     = "Function Minimization Without Evaluating 
                Derivatives --- {A} Review",
   JOURNAL   = "Comput. J.",
   VOLUME    = "8",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1983",
   PAGES     = "33--41",
   REFERRED  = "[Gayd91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Flet91a,
   AUTHOR    = "Fletcher, R. 
                and Hall, J. A. J.",
   TITLE     = "Ordering Algorithms for Irreducible Sparse Linear Systems",
   INSTITUTION = "Dundee University",
   MONTH     = "",
   YEAR      = "1991",
   TYPE      = "Report",
   NUMBER    = "NA/131",
   ADDRESS   = "Dundee, Scotland",
   REFERRED  = "[Dixo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Fore89b,
   AUTHOR    = "Forest, Etienne
                and Berz, Martin",
   TITLE     = "Canonical Integration and Analysis of Periodic Maps using
                {N}on-{S}tandard Analysis and {L}ie Methods",
   BOOKTITLE = "Lie Methods in Optics II",
   YEAR      = "1989",
   EDITOR    = "",
   PUBLISHER = "Springer Verlag",
   ADDRESS   = "Berlin",
   PAGES     = "47--66",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Fore89a,
   AUTHOR    = "Forest, Etienne
                and Berz, Martin
                and Irwin, John",
   TITLE     = "Normal form methods for complicated periodic systems: 
                {A} complete solution using differential algebra and 
                {L}ie operators",
   JOURNAL   = "Particle Accelerators",
   VOLUME    = "24",
   NUMBER    = "",
   YEAR      = "1989",
   PAGES     = "91 +",
   REFERRED  = "[Mich91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Four90a,
   AUTHOR    = "Fourer, R.
                and Gay, David M.
                and Kernighan, B. W.",
   TITLE     = "A Modeling Language for Mathematical Programming",
   JOURNAL   = "Management Science",
   VOLUME    = "36",
   NUMBER    = "5",
   YEAR      = "1990",
   PAGES     = "519--554",
   REFERRED  = "[Gayd91a]; [Jued91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Foxp78a,
   AUTHOR    = "P. A. Fox
                and A. D. Hall
                and N. L. Schryer",
   TITLE     = "The {\tt PORT} Mathematical Subroutine Library",
   JOURNAL   = "ACM Trans. Math. Software",
   VOLUME    = "4",
   NUMBER    = "",
   MONTH     = "June",
   YEAR      = "1978",
   PAGES     = "104--126",
   REFERRED  = "[Gayd91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Fran78a,
   AUTHOR    = "Frank, P. M.",
   TITLE     = "Introduction to System Sensitivity Theory",
   PUBLISHER = "Academic Press",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1978",
   REFERRED  = "[Worl91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Fras91a,
   AUTHOR    = "C. W. Fraser
                and D. R. Hanson",
   TITLE     = "A Retargetable Compiler for {ANSI} {C}",
   INSTITUTION = "Department of Computer Science, Princeton University",
   MONTH     = "February",
   YEAR      = "1991",
   TYPE      = "Research Report",
   NUMBER    = "CS--TR--303--91",
   ADDRESS   = "Princeton, N.J.",
   REFERRED  = "[Gayd91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Free88a,
   author    = "Timothy Freeman 
                and Gregory Imirzian 
                and Erich Kaltofen
                and Lakshman Yagati",
   title     = "Dagwood: {A} system of manipulating polynomials given 
                by straight-line programs",
   journal   = "ACM Trans. Math. Software",
   year      = "1988",
   pages     = "218--240",
   volume    = "14",
   month     = "September",
   number    = "3",
   REFERRED  = "[Char91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Garc79a,
   AUTHOR    = "Garc\'{\i}a, Oscar",
   TITLE     = "Modelling stand development with stochastic 
                differential equations",
   BOOKTITLE = "Mensuration for Management Planning of Exotic Forest 
                Plantations",
   YEAR      = "1979",
   EDITOR    = "Elliot, D. A.",
   PUBLISHER = "New Zealand Forest Service, FRI Symposium No. 20",
   ADDRESS   = "",
   PAGES     = "315--333",
   REFERRED  = "[Garc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}
 

@ARTICLE
{
   Garc83a,
   AUTHOR    = "Garc\'{\i}a, Oscar",
   TITLE     = "A stochastic differential equation model for the height 
                growth of forest stands",
   JOURNAL   = "Biometrics",
   VOLUME    = "39",
   NUMBER    = "",
   YEAR      = "1983",
   PAGES     = "1059--1072",
   REFERRED  = "[Garc91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Garc84a,
   AUTHOR    = "Garc\'{\i}a, Oscar",
   TITLE     = "New class of growth models for even-aged stands: 
                {\it {P}inus radiata} in {G}olden {D}owns {F}orest",
   JOURNAL   = "New Zealand J. Forestry Science",
   VOLUME    = "14",
   NUMBER    = "",
   YEAR      = "1984",
   PAGES     = "65--88",
   REFERRED  = "[Garc91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Garc88a,
   AUTHOR    = "Garc\'{\i}a, Oscar",
   TITLE     = "Experience with an advanced growth modelling methodology",
   BOOKTITLE = "Forest Growth Modelling and Prediction",
   YEAR      = "1988",
   EDITOR    = "Ek,  A. R.
                and Shifley, S. R.
                and Burk, T. E.",
   PUBLISHER = "USDA Forest Service, General Technical Report NC-120",
   ADDRESS   = "",
   PAGES     = "668--675",
   REFERRED  = "[Garc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}
 

@ARTICLE
{
   Garc88b,
   AUTHOR    = "Garc\'{\i}a, Oscar",
   TITLE     = "Growth modelling -- {A} (re)view",
   JOURNAL   = "New Zealand Forestry",
   VOLUME    = "33",
   NUMBER    = "",
   YEAR      = "1988",
   PAGES     = "14--17",
   REFERRED  = "[Garc91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Garc89a,
   AUTHOR    = "Garc\'{\i}a, Oscar",
   TITLE     = "Growth Modelling -- {N}ew Developments",
   BOOKTITLE = "Japan and New Zealand Symposium on Forestry Management 
                Planning",
   YEAR      = "1989",
   EDITOR    = "Nagumo, H.
                and Konohira, Y.",
   PUBLISHER = "Japan Association for Forestry Statistics",
   ADDRESS   = "",
   PAGES     = "",
   REFERRED  = "[Garc91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Garc91a,
   AUTHOR    = "Garc\'{\i}a, Oscar",
   TITLE     = "A System for the Differentiation of {F}ortran Code and an
                Application to Parameter Estimation in Forest Growth 
                Models",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "273--286",
   REFERRED  = "[Jued91a]; [Soul91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Gate85a,
   AUTHOR    = "Gates, B. L.",
   TITLE     = "{GENTRAN}: {A}n automatic code generation facility 
                for {REDUCE}",
   JOURNAL   = "ACM SIGSAM Bulletin",
   VOLUME    = "75",
   NUMBER    = "",
   YEAR      = "1985",
   PAGES     = " 24--85",
   REFERRED  = "[Gold91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Gate86a,
   AUTHOR    = "Gates, B. L.",
   TITLE     = "A numerical code generation facility for {REDUCE}",
   BOOKTITLE = "Proceedings of the 1986 Symposium on Symbolic and 
                Algebraic Computation",
   MONTH     = "July",
   YEAR      = "1986",
   EDITOR    = "Char, Bruce W.",
   PUBLISHER = "ACM Press",
   ADDRESS   = "New York",
   PAGES     = "94--99",
   REFERRED  = "[Char91a]; [Gold91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Gate87a,
   AUTHOR    = "Gates, B. L.",
   TITLE     = "{GENTRAN} User's Manual, {REDUCE} Version",
   PUBLISHER = "The RAND Corporation",
   SERIES    = "",
   ADDRESS   = "Santa Monica, Calif.",
   YEAR      = "1987",
   REFERRED  = "[Gold91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Gayd83a,
   AUTHOR    = "Gay, David M.",
   TITLE     = "{ALGORITHM} 611 --- {S}ubroutines for Unconstrained 
                Minimization Using a Model/Trust-Region Approach",
   JOURNAL   = "ACM Trans. Math. Software",
   VOLUME    = "9",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1983",
   PAGES     = "503--524",
   REFERRED  = "[Gayd91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Gayd91a,
   AUTHOR    = "Gay, David M.",
   TITLE     = "Automatic Differentiation of Nonlinear {AMPL} Models",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "61--73",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MISC
{
   Gayd91b,
   AUTHOR    = "Gay, David M.",
   TITLE     = "Response to electronic mail survey",
   HOWPUBLISHED = "Personal communication",
   MONTH     = "March",
   YEAR      = "1991",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Gibb60a,
   AUTHOR    = "Gibbons, A.",
   TITLE     = "A program for the automatic integration of differential
                equations using the method of {T}aylor series",
   JOURNAL    = "Comp. J.",
   VOLUME    = "3",
   YEAR      = "1960",
   PAGES     = "108--111",
   REFERRED  = "[Bart70a]; [Chan74a]; [Corl82a]; [Hali83a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; computer program; Taylor series.",
   ABSTRACT  = "This is a description of a Taylor series method.  The
                recurrence relations for simple functions are derived.
                Examples of how systems can be presented to an
                implementation of the theory are given.",
}


@ARTICLE
{
   Gilb92a,
   AUTHOR    = "Gilbert, J. Ch.",
   TITLE     = "Automatic Differentiation and Iterative Processes",
   JOURNAL   = "Optimization Methods and Software",
   VOLUME    = "1",
   NUMBER    = "",
   YEAR      = "1992",
   PAGES     = "13--21",
   REFERRED  = "",
   NOTE      = "Also appeared as Preprint, INRIA, Le Chesnay, France, 1991.",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@techreport
{
   Gilb91b,
   author     = "J. Ch. Gilbert 
                 and G. {Le Vey} 
                 and J. Masse",
   title      = "La diff\'erentiation automatique de fonctions 
                 repr\'esent\'ees par des programmes",
   type       = "Rapport de Recherche",
   number     = "1557",
   institution = "INRIA",
   address    = "BP 105, F-78153 Le Chesnay, France",
   year       = "1991",
}


@ARTICLE
{
   Gold84a,
   AUTHOR    = "Goldfarb, D.
                and Toint, P.",
   TITLE     = "Optimal estimation of {J}acobian and {H}essian matrices 
                that arise in finite difference calculations",
   JOURNAL   = "Mathematics of Computation",
   YEAR      = "1984",
   VOLUME    = "43",
   NUMBER    = "",
   PAGES     = "69--88",
   MONTH     = "",
   REFERRED  = "[Bisc91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}
 

@INCOLLECTION
{
   Gold91a,
   AUTHOR    = "Goldman, Victor V.
                and Molenkamp, J.
                and van Hulzen, J. A.",
   TITLE     = "Efficient Numerical Program Generation and Computer
                Algebra Environments",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "74--83",
   REFERRED  = "[Char91a]; [Garc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Gome90a,
   AUTHOR    = "Gomez, C.",
   TITLE     = "{MACROFORT}: {A} {FORTRAN} code generator for {MAPLE}",
   INSTITUTION = "INRIA",
   YEAR      = "1990",
   TYPE      = "Rapports Techniques",
   NUMBER    = "119",
   ADDRESS   = "",
   REFERRED  = "[Gold91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Grah75a,
   AUTHOR    = "Graham, Ron L.",
   TITLE     = "The Largest Small Hexagon",
   JOURNAL   = "J. Combinatorial Theory (A)",
   VOLUME    = "18",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1975",
   PAGES     = "165--170",
   REFERRED  = "[Gayd91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Gran88a,
   AUTHOR    = "L. Grandinetti
                and D. Conforti",
   TITLE     = "Numerical Comparisons of Nonlinear Programming
                Algorithms on Serial and Vector Processors Using
                Automatic Differentiation",
   JOURNAL   = "Mathematical Programming",
   VOLUME    = "42",
   NUMBER    = "",
   YEAR      = "1988",
   PAGES     = "375--389",
   REFERRED  = "",
   NOTE      = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "It is shown by numerical computation that real-world
                optimal electrical power flow problems can be solved 
                in real-time using vector processors.  These problems 
                are nonlinear optimization problems characterized by 
                highly nonlinear constraints and by a large number of
                variables, and cannot be solved in real-time, even on 
                mainframe computers.",
}


@INCOLLECTION
{
   Gray67a,
   AUTHOR    = "Gray, Julia H.
                and Rall Louis B.",
   TITLE     = "{NEWTON}: {A} general purpose program for solving nonlinear
                equations",
   BOOKTITLE = "Proc. 1967 Army Numerical Analysis Conference",
   PUBLISHER = "U.S. Army Research Office",
   ADDRESS   = "Research Triangle Park, N.C.",
   YEAR      = "1967",
   PAGES     = "11--59",
   REFERRED  = "[Kuba72a]; [Rall80a]; [Rall84a].",
   COMMENT   = "Also MRC Technical Summary Report No. 790, Mathematics
                Research Center, University of Madison-Wisconsin.",
   KEYWORDS  = "point algorithm; computer program; non-linear equations;
                differentiation arithmetic.",
   ABSTRACT  = "A program is described which uses Newton's method for
                solving a system of non-linear equations.  The Jacobian is
                calculated using differentiation arithmetic.  Automatic
                error analysis is provided by using differentiation
                arithmetic to calculate the Hessian.",
}


@TECHREPORT
{
   Gray67b,
   AUTHOR    = "Gray, Julia H.
                and Reiter, Allan",
   TITLE     = "A compiler of differentiable expressions {(CODEX)} for 
                the {CDC} 3600",
   TYPE      = "MRC Technical Summary Report",
   NUMBER    = "No. 791",
   INSTITUTION = "Mathematics Research Center,
                  University of Wisconsin - Madison",
   YEAR      = "1967",
   PAGES     = "",
   REFERRED  = "[Carl86a]; [Gray67a]; [Gray74a]; [Gray75a]; [Rall80a];
                [Rall84a]; [Reit67b].",
   COMMENT   = "",
   KEYWORDS  = "precompiler.",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Gray75a,
   AUTHOR    = "Gray, Julia H.
                and Rall, Louis B.",
   TITLE     = "{INTE}: {A} {UNIVAC} 1108/1110 Program for Numerical
                Integration with Rigorous Error Estimation",
   INSTITUTION = "Mathematics Research Center,
                  University of Wisconsin - Madison",
   YEAR      = "1975",
   TYPE      = "MRC Technical Summary Report",
   NUMBER    = "No. 1428",
   REFERRED  = "[Corl91a]; [Corl87a]; [Corl88a]; [Hali83a]; [Rall80a].",
   COMMENT   = "",
   KEYWORDS  = "interval algorithm; Euler-Maclaurin quadrature;
                differentiation arithmetic; computer program; error
                estimation.",
   ABSTRACT  = "The application of the Euler-Maclaurin formula for numerical
                integration can be automated by using software for interval
                analysis and differentiation arithmetic.  The interval
                techniques permit rigorous bounding of the error due to
                roundoff, and also the truncation error.  Optimal results
                for these bounds are developed to give a required accuracy
                in minimum time, or an estimate of the ultimate accuracy
                obtained using a UNIVAC 1108/1110 program.  (Paper
                abstract).",
}


@BOOK
{
   Gree76a,
   AUTHOR    = "Greenspan, E.",
   TITLE     = "Developments in Perturbation Theory",
   PUBLISHER = "Academic Press",
   SERIES    = "Advances in Nuclear Science and Technology",
   VOLUME    = "9",
   ADDRESS   = "New York",
   YEAR      = "1976",
   REFERRED  = "[Worl91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Grie88a,
    AUTHOR  = "Andreas Griewank",
    TITLE   = "Book Review of 
               {{\it Numerical Derivatives and Nonlinear Analysis}}",
    JOURNAL = "{SIAM Review}",
    YEAR    = "1988",
    VOLUME  = "30",
    NUMBER  = "2",
    PAGES   = "327--329",
    MONTH   = "June",
    COMMENT = "Book review -- note references given in this review.",
}


@INCOLLECTION
{
   Grie89a,
   AUTHOR    = "Griewank, Andreas",
   TITLE     = "On Automatic Differentiation",
   BOOKTITLE = "Mathematical Programming:
                Recent Developments and Applications",
   PUBLISHER = "Kluwer Academic Publishers",
   YEAR      = "1989",
   EDITOR    = "M. Iri
                and K. Tanabe",
   PAGES     = "83--108",
   ADDRESS   = "Dordrecht",
   REFERRED  = "[Bisc91a]; [Char91a]; [Corl91a]; [Dixo91a]; [Evtu91a]; 
                [Garc91a]; [Gayd91a]; [Gold91a]; 
                [Grie91a]; [Horw91a]; [Irim91a]; 
                [Jued91a]; [Kubo91a]; [Mazo91a]; [Navo91a];
                [Rall91a]; [Saar91a]; [Soul91a]; [Tesf91a]; [Thac91a].",
   NOTE      = "Also appeared as Preprint MCS--P10--1088,
                Mathematics and Computer Science Division,
                Argonne National Laboratory, Argonne, Ill.,
                October 1988.",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Grie90c,
   AUTHOR    = "Griewank, Andreas",
   TITLE     = "Direct Calculation of {N}ewton Steps without Accumulating 
                {J}acobians",
   BOOKTITLE = "Large-Scale Numerical Optimization",
   YEAR      = "1990",
   EDITOR    = "T. F. Coleman 
                and Yuying Li",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "115--137",
   NOTE      = "Also appeared as Preprint MCS--P132--0290,
                Mathematics and Computer Science Division,
                Argonne National Laboratory,
                Argonne, Ill., February 1990",
   REFERRED  = "[Dixo91a]; [Grie91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Grie91b,
   AUTHOR    = "Griewank, Andreas",
   TITLE     = "Achieving logarithmic growth of temporal and spatial 
                complexity in reverse automatic differentiation",
   JOURNAL    = "Optimization Methods and Software",
   VOLUME     = "",
   NUMBER     = "",
   YEAR       = "to appear",
   PAGES      = "",
   NOTE       = "Also appeared as Preprint MCS--P228--0491, 
                 Mathematics and Computer Science Division,
                 Argonne National Laboratory, Argonne, Ill., April 1991.",
   REFERRED  = "[Bisc91a]; [Kubo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Grie91c,
   AUTHOR    = "Griewank, Andreas",
   TITLE     = "Automatic Evaluation of First- and Higher-Derivative Vectors",
   BOOKTITLE = "Proceedings of the Conference at W{\"u}rzburg, Aug. 1990,
                Bifurcation and Chaos: {A}nalysis, Algorithms, Applications",
   PUBLISHER = "Birkh{\"a}user Verlag",
   YEAR      = "1991",
   VOLUME    = "97",
   EDITOR    = "R. Seydel
                and F. W. Schneider
                and T. K{\"u}pper
                and H. Troger",
   CHAPTER   = "",
   PAGES     = "135--148",
   ADDRESS   = "Basel, Switzerland",
   MONTH     = "",
   REFERRED  = "[Bisc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Grie91d,
   AUTHOR    = "Griewank, Andreas",
   TITLE     = "The Chain Rule Revisited in Scientific Computing",
   JOURNAL   = "SIAM News",
   VOLUME    = "24",
   NUMBER    = "",
   MONTH     = "May \& July",
   YEAR      = "1991",
   PAGES     = "",
   REFERRED  = "[Bisc91a]; [Kalm91a].",
   NOTE      = "no. 3, p. 20 \& no. 4, p. 8",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Grie91e,
   TITLE     = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = ""
}


@TECHREPORT
{
   Grie91f,
   AUTHOR = "Griewank, Andreas",
   TITLE  = "Sequential Evaluations of Adjoints and Higher
	     Derivative Vectors by Overloading and Reverse
	     Accumulation",
   INSTITUTION = "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin",
   YEAR      = "1991",
   MONTH     = "July",
   TYPE      = "Preprint",
   NUMBER    = "SC 91--3",
   ADDRESS   = "",
   REFERRED  = "[Corl91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Grie92a,
   AUTHOR    = "Griewank, Andreas
                and Juedes, David
                and Srinivasan, Jay
                and Tyner, Charles",
   TITLE     = "{ADOL-C}, A Package for the Automatic Differentiation
                of Algorithms Written in {C/C++}",
   JOURNAL    = "ACM Trans. Math. Software",
   VOLUME     = "",
   NUMBER     = "",
   YEAR       = "to appear",
   PAGES      = "",
   NOTE       = "Also appeared as Preprint MCS--P180--1190,
                 Mathematics and Computer Science Division,
                 Argonne National Laboratory, Argonne, Ill., November 1990.",
   REFERRED     = "[Bisc91a]; [Gayd91a]; [Gold91a]; [Grie91a]; 
                   [Jued91a]; [Kubo91a]; [Mich91a]; [Tesf91a].",
   COMMENT      = "",
   KEYWORDS     = "",
   ABSTRACT     = "",
}


@INCOLLECTION
{
   Grie91a,
   AUTHOR    = "Griewank, Andreas
                and Reese, Shawn",
   TITLE     = "On the Calculation of {J}acobian Matrices by the
                {M}arkowitz Rule",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   YEAR      = "1991",
   PAGES     = "126--135",
   REFERRED  = "[Corl91a]; [Irim91a].",
   NOTE      = "Also appeared as Preprint MCS--P267--1091,
                Mathematics and Computer Science Division,
                Argonne National Laboratory, Argonne, Ill.,
                January 1992.",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Hali83a,
   AUTHOR    = "Halin, Hans J.",
   TITLE     = "The applicability of {T}aylor series methods in simulation",
   BOOKTITLE = "Proceedings of the 1983 Summer Computer Simultation
                Conference (Vancouver, B.C.)",
   VOLUME    = "5",
   PUBLISHER = "",
   YEAR      = "1983",
   PAGES     = "",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "differentiation arithmetic; Taylor series; computer program;
                numerical results; convergence.",
   ABSTRACT  = "The author surveys historical and current developements in
                the application of recurrent Taylor series to the integration
                of systems of ordinary differential equations.  The historical
                developement of the subject is reviewed along with a discussion
                of the reasons for the existence of present day prejudice
                against the method.  A summary of current techniques is
                presented including those for deriving the recurrence
                relations with particular emphasise towards implementation.
                Questions about convergence, stepsize control and automatic
                control of series length are considered.  Various
                difficulties such as integration across discontinuities and
                implicit differential equations are discussed and accurate and
                efficient remedies are provided.  A simulation language, PSCSP
                (Power Series Continuous-system Simulation Program), is
                presented.  This is used as a medium for testing and comparing
                the theory discussed earlier.",
}


@ARTICLE
{
   Hall82a,
   AUTHOR    = "M. C. G. Hall 
                and D. G. Cacuci
                and M. E. Schlesinger",
   TITLE     = "Sensitivity analysis of a radiative-convective 
                model by the adjoint method",
   JOURNAL   = "J. Atmos. Sci.",
   VOLUME    = "39",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1982",
   PAGES     = "2038--2050",
   REFERRED  = "[Tala91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Hart67a,
   AUTHOR    = "Hartwell, J. G.",
   TITLE     = "Simultaneous integration of N-bodies by analytic
               continuation with recursively formed derivatives",
   JOURNAL   = "J. Astronomical Sci.",
   VOLUME    = "XIV",
   NUMBER    = "4",
   YEAR      = "1967",
   PAGES     = "173--177",
   REFERRED  = "[Chan74a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithms; differentiation arithmetic; Taylor series;
               numerical results.",
   ABSTRACT  = "The paper describes how to set up the recursion relations
               for the Taylor series method for the N-bodies problem.
               Numerical results are provided which compare the method for
               various tolerences and initial conditions."
}


@INCOLLECTION
{
   Haye87a,
   AUTHOR    = "Hayes, K. J.
                and Hirschberg, J. G.
                and Slottje, D. J.",
   TITLE     = "Computer Algebra: {S}ymbolic and Algebraic Computation
               in Economic/Econometric Applications",
   BOOKTITLE = "Advances in Econometrics",
   VOLUME    = "6",
   PUBLISHER = "JAI Press, Inc.",
   YEAR      = "1987",
   EDITOR    = "",
   CHAPTER   = "",
   PAGES     = "51--89",
   ADDRESS   = "",
   MONTH     = "",
   REFERRED  = "[Tesf91a]",
}


@BOOK
{
   Hear87a,
   AUTHOR    = "Hearn, A. C.",
   TITLE     = "{REDUCE} User's Manual, Version 3.3",
   PUBLISHER = "The Rand Corporation",
   SERIES    = "",
   ADDRESS   = "Santa Monica, Calif.",
   YEAR      = "1987",
   REFERRED  = "[Gold91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Hein71a,
   AUTHOR    = "Heintz, Wulff Dieter",
   TITLE     = "Doppelsterne",
   PUBLISHER = "Wilhelm Goldmann Verlag",
   SERIES    = "",
   ADDRESS   = "Munich",
   YEAR      = "1971",
   PAGES     = "55--73",
   REFERRED  = "[Soul91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Henr56a,
   AUTHOR    = "Henrici, Peter",
   TITLE     = "Automatic computations with power series",
   JOURNAL   = "J. ACM",
   VOLUME    = "3",
   NUMBER    = "1",
   YEAR      = "1956",
   PAGES     = "10--15",
   REFERRED  = "[Corl82a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithms; recursion relations.",
   ABSTRACT  = "The use of recursion relations in the calculation of power
               series is suggested.  The recursion relations for two
               example power series are given.",
}


@BOOK
{
   Henr64a,
   AUTHOR    = "Henrici, Peter",
   TITLE     = "Elements  of Numerical Analysis",
   PUBLISHER = "John Wiley and Sons",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1964",
   REFERRED  = "[Kubo91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Henr74a,
   AUTHOR    = "Henrici, Peter",
   TITLE     = "Applied and Computational Complex Analysis, Vol. 1",
   PUBLISHER = "John Wiley and Sons",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1974",
   REFERRED  = "[Flan91a]; [Rall91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Hert91a,
   AUTHOR    = "Hertz, J.
                and Krough, A.
                and Palmer, R.",
   TITLE     = "Introduction to the Theory of Neural Computation",
   PUBLISHER = "Addison-Wesley",
   SERIES    = "",
   ADDRESS   = "Reading, Mass.",
   YEAR      = "1991",
   REFERRED  = "[Saar91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Hill91a,
   AUTHOR    = "Hill, David R.
                and Rich, Lawrence C.",
   TITLE     = "Automatic Differentiation in {MATLAB}",
   JOURNAL   = "Applied Numerical Mathematics",
   VOLUME    = "9",
   NUMBER    = "",
   YEAR      = "1992",
   PAGES     = "33--43",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Hill82a,
   AUTHOR    = "Hillstrom, Kenneth E.",
   TITLE     = "{JAKEF} -- {A} portable symbolic differentiator of functions
               given by algorithms",
   TYPE      = "Technical Report",
   NUMBER    = "ANL--82--48",
   INSTITUTION = "Mathematics and Computer Science Division,
                Argonne National Laboratory",
   ADDRESS   = "Argonne, Ill.",
   YEAR      = "1982",
   REFERRED  = "[Arbe85a].",
   COMMENT   = "",
   KEYWORDS  = "symbolic differentiator; precompiler.",
   ABSTRACT  = "A precompiler, which is a {FORTRAN} version of that writen by
                Speelpenning [Spee80a], is described.",
}


@TECHREPORT
{
   Hill85a,
   AUTHOR    = "Hillstrom, K. E.",
   TITLE     = "Users Guide for {JAKEF}",
   INSTITUTION = "Mathematics and Computer Science Division,
                Argonne National Laboratory",
   ADDRESS   = "Argonne, Ill.",
   YEAR      = "1985",
   TYPE      = "Technical Memorandum",
   NUMBER    = "ANL/MCS--TM--16",
   REFERRED  = "[Corl91a]; [Garc91a]; [Gold91a]; [Irim91a]; 
                [Jued91a]; [Kubo91a]; [Soul91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Himm72a,
   AUTHOR    = "Himmelblau, D. M.",
   TITLE     = "Applied Nonlinear Programming",
   PUBLISHER = "McGraw-Hill",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1972",
   REFERRED  = "[Gayd91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MASTERSTHESIS
{
   Hort89a,
   AUTHOR    = "Horton, S.",
   TITLE     = "Numerical Derivatives: {A} Comparative Study",
   SCHOOL    = "Mathematics Department, University of Southern California",
   YEAR      = "1989",
   ADDRESS   = "Los Angeles, Calif. 90089",
   MONTH     = "",
   REFERRED  = "[Tesf91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Horw89b,
   AUTHOR    = "Horwedel, Jim E.",
   TITLE     = "Matrix Reduction Algorithms for {GRESS} and {ADGEN}",
   INSTITUTION = "Martin Marietta Energy Systems, Inc., 
                Oak Ridge National Laboratory",
   YEAR      = "1989",
   TYPE      = "Technical Memorandum",
   NUMBER    = "ORNL/TM 11261",
   ADDRESS   = "Oak Ridge, Tenn.",
   REFERRED  = "[Horw91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Horw91a,
   AUTHOR    = "Horwedel, Jim E.",
   TITLE     = "{GRESS}: {A} Preprocessor for Sensitivity Studies on 
                {F}ortran Programs",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "243--250",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = ""
}


@TECHREPORT
{
   Horw92a,
   AUTHOR    = "Horwedel, Jim E.",
   TITLE     = "Reverse Automatic Differentiation of Modular Fortran
                Programs",
   INSTITUTION = "Computing and Telecommunications Division,
                Oak Ridge National Laboratory",
   MONTH     = "March",
   YEAR      = "1992",
   TYPE      = "Technical Memorandum",
   NUMBER    = "ORNL/TM 12050",
   ADDRESS   = "Oak Ridge, Tenn.",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Horw88a,
   AUTHOR    = "Horwedel, Jim E.
                and Worley, Brian A.
                and Oblow, E. M.
                and Pin, F. G.",
   TITLE     = "{GRESS} version 1.0 Users Manual",
   INSTITUTION = "Martin Marietta Energy Systems, Inc., 
                Oak Ridge National Laboratory",
   YEAR      = "1988",
   TYPE      = "Technical Memorandum",
   NUMBER    = "ORNL/TM 10835",
   ADDRESS   = "Oak Ridge, Tenn.",
   REFERRED  = "[Gold91a]; [Horw91a]; [Irim91a]; [Jued91a]; [Soul91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Horw89a,
   AUTHOR    = "Horwedel, J. E.
                and Wright, R. Q.
                and Maerker, R. E.",
   TITLE     = "Sensitivity Analysis of {EQ3}",
   INSTITUTION = "Oak Ridge National Laboratory",
   YEAR      = "1990",
   TYPE      = "Technical Memorandum",
   NUMBER    = "ORNL/TM 11407",
   ADDRESS   = "Oak Ridge, Tenn.",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Horw90a,
   AUTHOR    = "Horwedel, J. E.
                and Raridon, R. J.
                and Wright, R. Q.",
   TITLE     = "Sensitivity Analysis of {AIRDOS--EPA} Using {ADGEN} 
                with Matrix Reduction Algorithms",
   INSTITUTION = "Martin Marietta Energy Systems, Inc., 
                Oak Ridge National Laboratory",
   YEAR      = "1989",
   TYPE      = "Technical Memorandum",
   NUMBER    = "ORNL/TM 11373",
   ADDRESS   = "Oak Ridge, Tenn.",
   REFERRED  = "[Corl91a]; [Horw91a]; [Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Houn92a,
   AUTHOR    = "Ian Hounam
                and Robert J. Iles
                and Stephens, Bruce R.",
   TITLE     = "The {DAPRE} Preprocessor Users' Guide ({UNIX} Version)",
   INSTITUTION = "Numerical Algorithms Group",
   MONTH     = "",
   YEAR      = "1992",
   TYPE      = "NAgWare user document",
   NUMBER    = "NP2299",
   ADDRESS   = "Oxford, UK",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Huss90a,
   AUTHOR    = "Huss, R.",
   TITLE     = "An {A}da Library for Automatic Evaluation of
                Derivatives",
   JOURNAL   = "Applied Mathematics and Computation",
   YEAR      = "1990",
   VOLUME    = "35",
   NUMBER    = "",
   PAGES     = "103--123",
   MONTH     = "January",
   NOTE      = "Also appeared as Working Paper, Hughes Aircraft 
                Company, February 1989.",
   REFERRED  = "[Kalm91a]; [Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MANUAL
{
   IBM90a,
   AUTHOR    = "IBM",
   TITLE     = "{IBM} High Accuracy Arithmetic - Extended Scientific
                Computation",
   ORGANIZATION = "IBM",
   ADDRESS   = "Mechanicsburg, Penn.",
   YEAR      = "1990",
   NOTE      = "IBM Publication No. SC33--6462--00.",
   REFERRED  = "[Corl91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Irim62a,
   AUTHOR    = "Iri, Masao",
   TITLE     = "Fundamentals of the algebraical and topological
                treatments of general information networks",
   JOURNAL   = "RAAG Memoirs, G-V",
   VOLUME    = "3",
   NUMBER    = "",
   YEAR      = "1962",
   PAGES     = "418--450",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Irim69a,
   AUTHOR    = "Iri, Masao",
   TITLE     = "Network Flow, Transportation and Scheduling 
                --- Theory and Algorithms",
   PUBLISHER = "Academic Press",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1969",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Irim84a,
   AUTHOR    = "Iri, Masao",
   TITLE     = "Simultanious Computation of Functions, Partial
                Derivatives and Estimates of Rounding
                Errors --- {C}omplexity and Practicality",
   JOURNAL   = "Japan J. Applied Mathematics",
   YEAR      = "1984",
   VOLUME    = "1",
   NUMBER    = "2",
   PAGES     = "223--252",
   REFERRED  = "[Corl91a]; [Evtu91a]; [Fisc91b]; [Horw91a]; 
                [Irim91a]; [Kubo91a]; [Rall91a]; [Thac91a].",
   COMMENT   = "",
   KEYWORDS  = "differentiation arithmetic; error estimates; algebraic
               complexity.",
   ABSTRACT  = "This paper proves theoretical results about the algebraic
               complexity involved in calculating the partial derivatives
               of a function.  It is shown that the algebraic complexity of
               computing a function of several variables and its partial
               derivatives with respect to all of the variables is at most
               a constant (four, five, six or seven which is independent of
               the number of variables) times as large as that of computing
               the function alone.  Furthermore, it is seen that a
               reasonable bound for the rounding error incurred in the
               final function value is ready to obtain once the function
               and its derivatives have been computed according to the
               procedure described."
}


@INCOLLECTION
{
   Irim91a,
   AUTHOR    = "Iri, Masao",
   TITLE     = "History of Automatic Differentiation and Rounding Estimation",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "1--16",
   REFERRED  = "[Grie91a]; [Kubo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Irim87a,
   AUTHOR    = "Iri, Masao
                and Kubota, K.",
   TITLE     = "Methods of Fast Automatic Differentiation
                and Applications",
   INSTITUTION = "Department of Mathematical Engineering and Information 
                Physics, Faculty of Engineering, University of Tokyo",
   YEAR      = "1987",
   TYPE      = "Research Memorandum",
   NUMBER    = "RMI 87 -- 02",
   ADDRESS   = "",
   REFERRED  = "[Evtu91a]; [Fisc91b]; [Gold91a]; [Irim91a]; 
                [Kubo91a]; [Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Irim88a,
   AUTHOR    = "Iri, Masao
                and Tsuchiya, T.
                and Hoshi, M.",
   TITLE     = "Automatic Computation of Partial Derivatives and
                Rounding Error Estimates with Applications to 
                Large-scale Systems of Nonlinear Equations",
   JOURNAL   = "J. Computational and Applied Mathematics",
   VOLUME    = "24",
   YEAR      = "1988",
   PAGES     = "365--392",
   REFERRED  = "[Corl91a]; [Irim91a]; [Kubo91a].",
   COMMENT   = "",
   NOTE      = "Original Japanese version appeared in {\it J. 
                Information Processing}, 26 (1985), 
                pp.~1411--1420.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Isaa66a,
   AUTHOR    = "E. Isaacson 
                and Herb B. Keller",
   TITLE     = "Analysis of Numerical Methods",
   PUBLISHER = "John Wiley and Sons",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1966",
   REFERRED  = "[Shah91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MASTERSTHESIS
{
   Iwat84a,
   AUTHOR    = "Iwata, N.",
   TITLE     = "Automatization of the Computation of Partial Derivatives",
   SCHOOL    = "Graduate School, University of Tokyo",
   YEAR      = "1984",
   ADDRESS   = "",
   MONTH     = "",
   REFERRED  = "[Jued91a]; [Kubo91a].",
   NOTE      = "(In Japanese).",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Iwat83a,
   AUTHOR    = "Iwata, N.
                and Iri, Masao",
   TITLE     = "Computation of the gradient of a function with many variables",
   BOOKTITLE = "Papers of the Special Interest Group on Numerical Analysis",
   YEAR      = "1983",
   EDITOR    = "",
   PUBLISHER = "Information Processing Society of Japan, 7-1",
   ADDRESS   = "",
   PAGES     = "1--10",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Jack86a,
   AUTHOR    = "Jackson, R.H.F. 
                and McCormick, G.P.",
   TITLE     = "The polyadic structure of factorable function tensors with
                applications to high-order minimization techniques",
   JOURNAL   = "J. Opt. Theory Appl.",
   VOLUME    = "51",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1986",
   PAGES     = "63--94",
   REFERRED  = "[Fisc91b].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Jacq65a,
   AUTHOR    = "P. Jacquard 
                and C. Jain",
   TITLE     = "Permeability Distributions from Field Pressure Data",
   JOURNAL   = "Society of Petroleum Engineers J.",
   VOLUME    = "",
   NUMBER    = "",
   MONTH     = "December",
   YEAR      = "1965",
   PAGES     = "281--294",
   REFERRED  = "[Shah91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MANUAL
{
   JIS82a,
   AUTHOR    = "{Japanese Industrial Standard}",
   TITLE     = "Programming Language {FORTRAN}, {C6201 -- 1982}",
   ORGANIZATION = "",
   ADDRESS   = "",
   YEAR      = "1982",
   REFERRED  = "[Kubo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Jerr89a,
   AUTHOR    = "Jerrell, M.",
   TITLE     = "Automatic Differentiation and Function Minimization in {C++}",
   BOOKTITLE = "Proceedings of {OOP--SLA}",
   YEAR      = "1989",
   EDITOR    = "",
   PUBLISHER = "ACM Press",
   CHAPTER   = "",
   PAGES     = "18--24",
   ADDRESS   = "New York",
   MONTH     = "",
   REFERRED  = "[Jued91a]; [Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Jerr89b,
   AUTHOR    = "Jerrell, M.",
   TITLE     = "Automatic Differentiation Using Almost Any Language",
   JOURNAL   = "ACM SIGNUM Newsletter",
   VOLUME    = "",
   NUMBER    = "",
   YEAR      = "1989",
   PAGES     = "2--9",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Jerr90a,
   AUTHOR    = "Jerrell, M.",
   TITLE     = "Automatic Differentiation Using {C++}",
   JOURNAL   = "J. Object Oriented Programming",
   VOLUME    = "",
   NUMBER    = "",
   YEAR      = "1990",
   PAGES     = "17--24",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   John75a,
   AUTHOR    = "Johnson, S. C.",
   TITLE     = "{YACC} --- {Y}et Another Compiler - Compiler",
   INSTITUTION = "Bell Laboratories",
   YEAR      = "1975",
   TYPE      = "Computing Science Technical Report",
   NUMBER    = "No. 32",
   ADDRESS   = "Murray Hill, N.J.",
   REFERRED  = "[Kubo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Jone91a,
   AUTHOR    = "Jones, M. T.
                and Plassmann, P. E.",
   TITLE     = "A Parallel Graph Coloring Heuristic",
   INSTITUTION = "Mathematics and Computer Science Division,
             Argonne National Laboratory",
   MONTH     = "June",
   YEAR      = "1991",
   TYPE      = "Preprint",
   NUMBER    = "MCS--P246-0691",
   ADDRESS   = "Argonne, Ill.",
   REFERRED  = "[Bisc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@PHDTHESIS
{
   Joss76a,
   AUTHOR    = "Joss, Johan",
   TITLE     = "Algorithmisches Differenzieren",
   SCHOOL    = "Eidgenoessische Technische Hochschule",
   ADDRESS   = "Z{\"u}rich, Switzerland",
   YEAR      = "1976",
   REFERRED  = "[Spee80a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; precompiler; computer program; numerical
               results.",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Jued91a,
   AUTHOR    = "Juedes, David",
   TITLE     = "A Taxonomy of Automatic Differentiation Tools",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "315--329",
   REFERRED  = "[Bisc91a]; [Garc91a]; [Irim91a]; [Kubo91a]; 
                [Mazo91a]; [Worl91a].",
   NOTE      = "Also appeared as Preprint MCS--P265--0991,
                Mathematics and Computer Science Division,
                Argonne National Laboratory,
                Argonne, Ill., September 1991.",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Jued90a,
   AUTHOR    = "Juedes, David
                and Griewank, Andreas",
   TITLE     = "Implementing Automatic Differentiation Efficiently",
   INSTITUTION = "Mathematics and Computer Sciences Division, 
                Argonne National Laboratory",
   YEAR      = "1990",
   TYPE      = "Technical Memorandum",
   NUMBER    = "ANL/MCS--TM--140",
   ADDRESS   = "Argonne, Ill.",
   MONTH     = "",
   REFERRED  = "[Bisc91a]; [Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kaba87a,
   AUTHOR    = "Kabaya, K.
                and Iri, Masoa",
   TITLE     = "Sum of uniformly distributed random variables and 
                family of nonanalytic ${C}^\infty$-functions",
   JOURNAL   = "Japan J. Applied Mathematics",
   VOLUME    = "4",
   NUMBER    = "",
   YEAR      = "1987",
   PAGES     = "1--22",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kaba88a,
   AUTHOR    = "Kabaya-Imai, K.
                and Iri, Masoa",
   TITLE     = "On operators defining a family of nonanalytic 
                ${C}^\infty$-functions",
   JOURNAL   = "Japan J. Applied Mathematics",
   VOLUME    = "5",
   NUMBER    = "",
   YEAR      = "1988",
   PAGES     = "333--365",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Kagi85a,
   AUTHOR    = "Kagiwada, Harriet
                and Kalaba, Robert
                and Rasakhoo, Nima
                and Spingarn Karl",
   TITLE     = "Numerical Derivatives and Nonlinear Analysis",
   PUBLISHER = "Plenum Press, Inc.",
   YEAR      = "1985",
   VOLUME    = "31",
   SERIES    = "Mathematical Concepts and Methods in Science and Engineering",
   ADDRESS   = "New York",
   REFERRED  = "MR 87g 65002; [Corl88a]; [Neid87a]; [Neid89a]; [Tesf91a].",
   COMMENT   = "Lower level treatment than [Rall81a] of automatic
                differentiation.  Lacks concept of a coder.  More detailed
                examples with programs.  Reviewed in SIAM Review by Andreas
                Griewank -- not a great book",
   KEYWORDS  = "automatic differentiation.",
   ABSTRACT  = "The authors survey automatic differentiation by the FEED
                (Fast and Efficient Evaluation of Derivatives) method and
                its applications.  The user writes programs consisting of
                subroutine calls.  The subroutines perform the necessary
                differentiation arithmetic.  Applications include Newton and
                Halley methods for rootfinding, nonlinear least squares,
                optimal control of two point boundary value problems using
                Newton-Raphson and gradient methods, system identification,
                Sukhanov's variable initial value method for boundary value
                problems, and nonlinear integral equations.  Most examples
                include Fortran or Basic programs.  The FEED method is used
                to compute the derivatives required by a method, but no
                Taylor series techniques are illustrated."
}


@MastersThesis
{
   Kahr53a,
   author    = "H. G. Kahrimanian",
   title     = "Analytical Differentiation by a Digital Computer",
   school    = "Temple University",
   year      = "1953",
   month     = "May",
   REFERRED  = "[Char91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kala81a,
   AUTHOR    = "Kalaba, R.
                and Tesfatsion, Leigh",
   TITLE     = "Complete Comparative Static Differential Equations",
   JOURNAL   = "Nonlinear Analysis: Theory, Methods, and Applications",
   YEAR      = "1981",
   VOLUME    = "5",
   NUMBER    = "",
   PAGES     = "821--833",
   MONTH     = "",
   REFERRED  = "[Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kala83a,
   AUTHOR    = "Kalaba, Robert
                and Tesfatsion, Leigh
                and Wang, J. L.",
   TITLE     = "A Finite Algorithm for the Exact Evaluation of
                Higher-Order Partial Derivatives of Functions of
                Many Variables",
   JOURNAL   = "J. Mathematical Analysis and Applications",
   VOLUME    = "92",
   YEAR      = "1983",
   PAGES     = "552--563",
   MONTH     = "",
   REFERRED  = "[Mich91a]; [Tesf91a]; [Wexl87a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; differentiation arithmetic.",
   ABSTRACT  = "An algorithm is presented which is a systematic extension of
                the algorithm presented in [Weng64a].  This allows the
                calculation of arbitrarily high orders of partial
                derivatives of functions of many variables.  The method does
                not take advantage of sparsity in any way, but the authors
                mention that it might be possible to do so.",
}


@ARTICLE
{
   Kala83b,
   AUTHOR    = "Kalaba, Robert
                and Tishler, A.",
   TITLE     = "A generalised {N}ewton algorithm using higher-order
                derivatives",
   JOURNAL    = "J. Opt. Theory and Appl.",
   VOLUME    = "39",
   NUMBER     = "1",
   PUBLISHER = "",
   YEAR      = "1983",
   PAGES     = "1--17",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; differentiation arithmetic; root finding.",
   ABSTRACT  = "A Newton-type algorithm which uses first to rth order
                partial derivatives is described.  This reduces to the
                Newton-Raphson algorithm if $ r = 2 $ .  The partial
                derivatives are calculated using the table method described
                in [Kala83a].  A specific example is given to show that the
                convergence of the method is faster than that of the
                standard Newton-Raphson algorithm.",
}


@ARTICLE
{
   Kala86a,
   AUTHOR    = "Kalaba, R.
                and Tesfatsion, Leigh",
   TITLE     = "Automatic Differentiation of Functions of Derivatives",
   JOURNAL   = "Computers and Mathematics with Applications",
   YEAR      = "1986",
   VOLUME    = "12A",
   NUMBER    = "11",
   PAGES     = "1091--1103",
   MONTH     = "November",
   REFERRED  = "[Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kala90a,
   AUTHOR    = "Kalaba, R.
                and Tesfatsion, Leigh",
   TITLE     = "Nonlocal Automated Sensitivity Analysis",
   JOURNAL   = "Computers and Mathematics with Applications",
   YEAR      = "1990",
   VOLUME    = "20",
   NUMBER    = "",
   PAGES     = "53--65",
   MONTH     = "",
   REFERRED  = "[Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kala91a,
   AUTHOR    = "Kalaba, R.
                and Tesfatsion, Leigh",
   TITLE     = "Solving Nonlinear Equations by Adaptive Homotopy Continuation",
   JOURNAL   = "Applied Mathematics and Computation",
   YEAR      = "1991",
   VOLUME    = "41",
   NUMBER    = "",
   PAGES     = "99--115",
   MONTH     = "",
   REFERRED  = "[Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kala81b,
   AUTHOR    = "Kalaba, R.
                and Tesfatsion, Leigh
                and Wang, J. L.",
   TITLE     = "Local and Nonlocal Comparative Static Analysis of
                Economic Systems",
   JOURNAL   = "Applied Mathematics and Computation",
   YEAR      = "1981",
   VOLUME    = "9",
   NUMBER    = "",
   PAGES     = "227--234",
   MONTH     = "",
   REFERRED  = "[Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kala87a,
   AUTHOR    = "Kalaba, R.
                and Plum, T.
                and Tesfatsion, Leigh",
   TITLE     = "Automation of Nested Matrix and Derivative Operations",
   JOURNAL   = "Applied Mathematics and Computation",
   YEAR      = "1987",
   VOLUME    = "23",
   NUMBER    = "",
   PAGES     = "243--268",
   MONTH     = "",
   REFERRED  = "[Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kala84a,
   AUTHOR    = "Kalaba, R.
                and Tischler, A.",
   TITLE     = "Automatic Derivative Evaluation in the Optimization of
                Nonlinear Models",
   JOURNAL   = "The Review of Economics and Statistics",
   YEAR      = "1984",
   VOLUME    = "66",
   NUMBER    = "",
   PAGES     = "653--660",
   MONTH     = "",
   REFERRED  = "[Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Kalm91a,
   AUTHOR    = "Kalman, Dan
                and Lindell, Robert",
   TITLE     = "Automatic Differentiation in Astrodynamical Modeling",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "228--243",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Kalm92a,
   AUTHOR    = "Kalman, Dan
                and Lindell, Robert",
   TITLE     = "Automatic Differentiation in Astrodynamical Modeling",
   INSTITUTION = "The Aerospace Corporation, Engineering and Technology
                Group",
   MONTH     = "March",
   YEAR      = "1992",
   TYPE      = "Aerospace Report",
   NUMBER    = "ATR--92(8151)--1",
   ADDRESS   = "El Segundo, Calif.",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kalt88a,
   author    = "Erich Kaltofen",
   title     = "Greatest common divisors of polynomials given by 
                straight-line programs",
   journal   = "J. ACM",
   year      = "1988",
   volume    = "35",
   number    = "1",
   pages     = "231--264",
   REFERRED  = "[Char91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Kalt89a,
   author    = "Erich Kaltofen",
   title     = "Factorization of polynomials given by straight-line 
                programs",
   booktitle = "Randomness in Computation",
   publisher = "JAI Press Inc.",
   year      = "1989",
   editor    = "S. Micali",
   pages     = "375--412",
   volume    = "5",
   series    = "Advances in Computing Research",
   address   = "Greenwich, Conn.",
   REFERRED  = "[Char91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Kalt90b,
   AUTHOR    = "Erich Kaltofen 
                and Michael F. Singer",
   TITLE     = "Size Efficient Parallel Algebraic Circuits for 
                Partial Derivatives",
   INSTITUTION = "Department of Computer Science,
                Rensselaer Polytechnic Institute",
   MONTH     = "October",
   YEAR      = "1990",
   TYPE      = "Technical Report",
   NUMBER    = "No. 90-32",
   ADDRESS   = "Troy, N.Y.",
   REFERRED  = "",
   COMMENT   = "",
   NOTE      = "To appear in World Scientific Publishing 
               Co. (Singapore) in the Proceedings of the IV International 
               Conference on Computer Algebra in Physical Research, held 
               at Dubna in the Soviet Union in May 1990.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@Article
{
   Kalt90a,
   author    = "Erich Kaltofen 
                and Barry Trager",
   title     = "Computing with Polynomials Given by Black Boxes for 
                Their Evaluations:  {G}reatest Common Divisors, 
                Factorization, Separation of Numerators and Denominators",
   journal   = "J. Symbolic Computation",
   year      = "1990",
   volume    = "9",
   number    = "3",
   pages     = "301--320",
   REFERRED  = "[Char91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}
 

@ARTICLE
{
   Kant57a,
   AUTHOR    = "Kantorovich, L. V.",
   TITLE     = "Ob Odno{\u\i} Matematichesko{\u\i} Simvolike, 
                Udobno{\u\i} pri Provedenii Vychisleni{\u\i} na Mashinakh",
   JOURNAL   = "Doklady Akademii Nauk. SSSR",
   VOLUME    = "113",
   NUMBER    = "4",
   YEAR      = "1957",
   PAGES     = "738--741",
   REFERRED  = "[Irim91a]; [Kubo91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Kauc84a,
   AUTHOR    = "Kaucher, Edgar W.
                and Miranker, Willard L.",
   TITLE     = "Self-Validating Numerics for Function Space Problems 
                --- {C}omputation with Guarantees for Differential 
                and Integral Equations",
   PUBLISHER = "Academic Press",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1984",
   REFERRED  = "[Irim91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kede80a,
   AUTHOR    = "Kedem, G.",
   TITLE     = "Automatic Differentiation of Computer Programs",
   JOURNAL   = "ACM Trans. Math. Software",
   MONTH     = "June",
   YEAR      = "1980",
   VOLUME    = "6",
   NUMBER    = "2",
   PAGES     = "150--165",
   REFERRED  = "[Garl85a] \# 706; [Arbe85a]; [Carl86a];
                [Corl82a]; [Corl88a]; [Corl91a]; [Crar79a]; [Fisc91b; 
                [Irim91a]; [Hali83a]; [Hill82a]; [Mich91a];
                [Pfei87a]; [Rall80a]; [Rall81a]; [Rall84a]; [Spee80a];
                [Tesf91a]; [Voli85a]; [Wexl87a].",
   COMMENT   = "Also appeared as {\sl Mathematics Research Center Technical
                Summary No. 1697,\/} University of Wisconsin - Madison,
                1976; and {\sl Proc. 1977 Army Numerical Analysis and
                Computer Conf.\/}, Madison, Wisc. 1977.",
   KEYWORDS  = "automatic differentiation; Fortran subprograms.",
   ABSTRACT  = "The author discusses how functions written in high level
                languages can be automatically differentiated.  The set of
                functions allowed is restricted to a class called {\sl
                piecewise factorable functions \}.  With this class of
                functions it is shown how to construct both Taylor series
                expansions and gradient calculations of the functions.  With
                the use of the precompiler AUGMENT it is shown how to
                implement both of these.  This is the first publication in
                English on the subject of autometic differentiation of
                programs.  Earlier work includes [Joss76a].",
}


@ARTICLE
{
   Kill85a,
   AUTHOR    = "Killingsworth, J. P.",
   TITLE     = "Microcomputer Calculations in Physics",
   JOURNAL   = "Reports on Progress in Physics",
   YEAR      = "1985",
   VOLUME    = "48",
   NUMBER    = "",
   PAGES     = "54--99",
   MONTH     = "",
   REFERRED  = "[Tesf91a].",
}


@ARTICLE
{
   Kimk84a,
   AUTHOR    = "Kim, K. V.
                and Nesterov, Yu E.
                and Cherkasski{\u\i}, B. V.",
   TITLE     = "Otsenka Trudo\'{e}mkosti Vychisleniya Gradienta",
   JOURNAL   = "Doklady Akademii Nauk. SSSR",
   VOLUME    = "275",
   NUMBER    = "6",
   YEAR      = "1984",
   PAGES     = "1306--1309",
   REFERRED  = "[Kubo91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kimk84b,
   AUTHOR    = "Kim, K. V.
                and Nesterov, Yu E.
                and Skokov, V. A.
                and Cherkasski{\u\i}, B. V.",
   TITLE     = "\` Effektivny{\u\i} Algoritm Vychisleniya 
                Proizvodnykh i \` Ekstremal'nye Zadachi",
   JOURNAL   = "\` Ekonomika i Matematicheskie Metody",
   VOLUME    = "20",
   NUMBER    = "2",
   YEAR      = "1984",
   PAGES     = "309--318",
   REFERRED  = "[Irim91a]; [Kubo91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kimk85a,
   AUTHOR    = "Kim, K. V.
                and Nesterov, Yu E.
                and Skokov, V. A.
                and Cherkasski{\u\i}, B. V.",
   TITLE     = "An Efficient Algorithm for Computing
                Derivatives and Extremal Problems",
   JOURNAL   = "MATEKON",
   VOLUME    = "21",
   NUMBER    = "",
   YEAR      = "1985",
   PAGES     = "49--67",
   REFERRED  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Klat91a,
   AUTHOR    = "Klatte, R.
                and Kulisch, U.
                and Neaga, M.
                and Ratz, D.
                and Ullrich, Ch.",
   TITLE  = "{PASCAL-XSC}: {A} {PASCAL} Extension for Scientific Computation",
   PUBLISHER = "Springer Verlag",
   YEAR      = "1991",
   VOLUME    = "",
   SERIES    = "",
   ADDRESS   = "Berlin",
   NOTE      = "",
   REFERRED  = "[Corl91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Knap68a,
   AUTHOR    = "Knapp, H.
                and Wanner, G.",
   TITLE     = "Numerical solution of ordinary differential equations by
                {G}roebner's method of {L}ie-series",
   TYPE      = "Technical Summary Report",
   NUMBER    = "No. 880",
   INSTITUTION = "Mathematics Research Center,
                University of Wisconsin - Madison",
   YEAR      = "1968",
   REFERRED  = "[Hali83a]; [Rall80a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; automatic differentiation; Lie series.",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Knap68b,
   AUTHOR    = "Knapp, H.
                and Wanner, G.",
   TITLE     = "{LIESE}: {A} program for ordinary differential equations using
                {L}ie-series",
   TYPE      = "Technical Summary Report",
   NUMBER    = "No. 881",
   INSTITUTION = "Mathematics Research Center,
                University of Wisconsin - Madison",
   YEAR      = "1968",
   PAGES     = "",
   REFERRED  = "[Hali83a]; [Rall80a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; automatic differentiation; Lie series.",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Knap69a,
   AUTHOR    = "Knapp, H.
                and Wanner, G.",
   TITLE     = "{LIESE II}: {A} program for ordinary differential 
                equations using {L}ie-series",
   TYPE      = "Technical Summary Report",
   NUMBER    = "No. 1008",
   INSTITUTION = "Mathematics Research Center,
                University of Wisconsin - Madison",
   YEAR      = "1969",
   PAGES     = "",
   REFERRED  = "[Gray74a]; [Gray75a]; [Hali83a]; [Kuba72a]; [Rall80a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; automatic differentiation; Lie series.",
   ABSTRACT  = "",
}


@BOOK
{
   Knut81a,
   AUTHOR    = "Donald E. Knuth",
   TITLE     = "The Art of Computer Programming, Vol. 2.
                Seminumerical Algorithms",
   PUBLISHER = "Addison-Wesley",
   SERIES    = "",
   ADDRESS   = "Reading, Mass.",
   YEAR      = "1981",
   REFERRED  = "[Laws91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Krin84a,
   AUTHOR    = "Krinsky, B.
                and Thames, Joseph",
   TITLE     = "The Structure of Synthetic Calculus",
   BOOKTITLE = "Proceedings of the International Workshop on High-Level 
                Computer Architecture, University of Maryland",
   PUBLISHER = "",
   YEAR      = "1984",
   PAGES     = "",
   REFERRED  = "[Tham91a]; [Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Kuba72a,
   AUTHOR    = "Kuba, Dennis
                and Rall Louis B.",
   TITLE     = "A {UNIVAC} 1108 program for obtaining rigorous error estimates
                for approximate solutions of systems of equations",
   TYPE      = "Technical Summary Report",
   NUMBER    = "No. 1168",
   INSTITUTION = "Mathematics Research Center,
                University of Wisconsin - Madison",
   YEAR      = "1972",
   PAGES     = "",
   REFERRED  = "[Gray75a]; [Rall84a].",
   COMMENT   = "",
   KEYWORDS  = "interval algorithm; root finding; error estimates; computer
                program; differentiation arithmetic.",
   ABSTRACT  = "A computer program is described which obtains, by use of
                interval arithmetic, rigorous error bounds for approximate
                solutions of finite systems of nonlinear equations.  The error
                bounds obtained include the contributions of truncation error
                for Newton's method, round-off error, and possible errors in
                the coefficients of the given system of equations."
}


@INCOLLECTION
{
   Kubo88a,
   AUTHOR    = "Kubota, Koichi",
   TITLE     = "A Preprocessor for Fast Automatic Differentiation
                --- {A}pplications and Difficulties on Practical Problems",
   BOOKTITLE = "{RIMS} {K}okyuroku 648 ``Fundamental Numerical Algorithms 
                and their Software''",
   YEAR      = "1988",
   EDITOR    = "",
   PUBLISHER = "Research Institute for Mathematical Sciences,
                Kyoto University",
   ADDRESS   = "",
   PAGES     = "",
   REFERRED  = "[Kubo91a].",
   NOTE      = "(In Japanese).",
   COMMENT   = "",
   ABSTRACT  = "",
}


@PHDTHESIS
{
   Kubo89a,
   AUTHOR    = "Kubota, Koichi",
   TITLE     = "Fast Automatic Differentiation and Applications",
   SCHOOL    = "Division of Engineering of the Graduate School of the 
                University of Tokyo",
   ADDRESS   = "",
   YEAR      = "1989",
   REFERRED  = "[Irim91a]; [Kubo91a].",
   NOTE      = "(In Japanese).",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Kubo91a,
   AUTHOR    = "Kubota, Koichi",
   TITLE     = "{PADRE2}, A {FORTRAN} Precompiler Yielding Error Estimates and
                Second Derivatives",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "251--262",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kubo88b,
   AUTHOR    = "Kubota, Koichi
                and Iri, Masao",
   TITLE     = "Formulation of Fast Automatic Differentiation and 
                the Analysis of its Complexity",
   JOURNAL   = "Transactions of Information Processing Society of Japan",
   VOLUME    = "29",
   NUMBER    = "",
   YEAR      = "1988",
   PAGES     = "551--560",
   REFERRED  = "[Irim91a]; [Kubo91a].",
   NOTE      = "(In Japanese).",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kubo89b,
   AUTHOR    = "Kubota, Koichi
                and Iri, Masao",
   TITLE     = "Estimates of Rounding Errors with Fast Automatic 
                Differentiation and Interval Analysis",
   JOURNAL   = "Transactions of Information Processing Society of Japan",
   VOLUME    = "30",
   NUMBER    = "",
   YEAR      = "1989",
   PAGES     = "807--815",
   REFERRED  = "[Irim91a]; [Kubo91a].",
   NOTE      = "(In Japanese).  English version is [Kubo91b].",
   COMMENT   = "Earlier English version is available as 
                {\it Research Memorandum} RMI 88--12,
                Department of Mathematical Engineering and Instrumentation 
                Physics, Faculty of Engineering, University of Tokyo, 1988.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Kubo90a,
   AUTHOR    = "Kubota, Koichi
                and Iri, Masao",
   TITLE     = "{PADRE2}, Version 1 --- {U}ser's Manual",
   INSTITUTION = "Department of Mathematical Engineering and Information 
                Physics, Faculty of Engineering, University of Tokyo",
   YEAR      = "1990",
   TYPE      = "Research Memorandum",
   NUMBER    = "RMI 90--01",
   ADDRESS   = "",
   REFERRED  = "[Jued91a]; [Kubo91a]; [Soul91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kubo91b,
   AUTHOR    = "Kubota, Koichi
                and Iri, Masao",
   TITLE     = "Estimates of Rounding Errors with Fast Automatic 
                Differentiation and Interval Analysis",
   JOURNAL   = "Journal of Information Processing",
   VOLUME    = "14",
   NUMBER    = "4",
   YEAR      = "1991",
   PAGES     = "508--515",
   REFERRED  = "",
   NOTE      = "English version of [Kubo89b].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Kuli86a,
   AUTHOR    = "Kulisch, Ulrich W. 
                and Miranker, Willard L.",
   TITLE     = "The arithmetic of the digital computer: {A} new approach",
   JOURNAL   = "SIAM Review",
   VOLUME    = "28",
   NUMBER    = "1",
   YEAR      = "1986",
   PAGES     = "1--40",
   REFERRED  = "[Layn91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Laca88a,
   AUTHOR    = "J. F. Lacarra 
                and Olivier Talagrand",
   TITLE     = "Short-Range Evolution of Small Perturbations 
                in a Barotropic Model",
   JOURNAL   = "Tellus",
   VOLUME    = "40A",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1988",
   PAGES     = "81--95",
   REFERRED  = "[Tala91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Lana81a,
   AUTHOR    = "Douglas H. Lanam",
   TITLE     = "An algebraic front-end for the production and use 
                of numeric programs",
   BOOKTITLE = "Proceedings of the 1981 Symposium on Symbolic and 
                Algebraic Computation",
   YEAR      = "1981",
   EDITOR    = "P. S. Wang",
   PAGES     = "223--227",
   ORGANIZATION = "Association of Computing Machinery",
   ADDRESS   = "New York",
   MONTH     = "August",
   REFERRED  = "[Char91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}
 

@ARTICLE
{
   Lars78a,
   AUTHOR    = "J. L. Larson 
                and A. H. Sameh",
   TITLE     = "Efficient calculation of the effects of roundoff errors",
   JOURNAL   = "ACM Trans. Math. Software",
   YEAR      = "1978",
   VOLUME    = "4",
   NUMBER    = "3",
   PAGES     = "228--236",
   MONTH     = "September",
   REFERRED  = "[Char91a].",
   COMMENT   = "Char -- First paper by Larson.  Gives algorithm used 
                in [Lars80a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@article
{
   Lars80a,
   AUTHOR    = "J. L. Larson 
                and A. H. Sameh",
   TITLE     = "Algorithms for Roundoff Error Analysis --- {A} Relative 
                Error Approach",
   JOURNAL   = "Computing",
   YEAR      = "1980",
   VOLUME    = "24",
   NUMBER    = "4",
   PAGES     = "275--297",
   REFERRED  = "",
   COMMENT   = "Char -- Summary of Larson's thesis [Lars78a] which 
                describes complete error analyses which use Bauer's 
                computational graphs.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Laws71a,
   AUTHOR    = "Lawson, Charles L.",
   TITLE     = "Computing Derivatives Using {W}-Arithmetic and {U}-Arithmetic",
   INSTITUTION = "Jet Propulsion Laboratory",
   ADDRESS   = "Pasadena, Calif.",
   MONTH     = "September",
   YEAR      = "1971",
   TYPE      = "Internal Computing Memorandum",
   NUMBER    = "CM--286",
   REFERRED  = "[Jued91a]; [Laws91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Laws88a,
   AUTHOR    = "Lawson, Charles L.",
   TITLE     = "Series reversion as the reversed chain rule",
   JOURNAL   = "ACM SIGNUM Newsletter",
   VOLUME    = "23",
   NUMBER    = "1",
   PUBLISHER = "",
   MONTH     = "January",  
   YEAR      = " 1988",
   PAGES     = "7--9",
   REFERRED  = "[Laws91a].",
   COMMENT   = "",
   KEYWORDS  = "differentiation arithmetic; implicit functions.",
   ABSTRACT  = "Lawson gives Fortran subroutines for differentiation
               arithmetic. A subroutine SWPRO for products corresponds to
               Chang's ATS [Chang74a].  The chain rule is implemented by
               repeated calls to SWPRO.  Series reversion for implicit
               functions is implemented by reversing the chain rule.  An
               application is given to Keppler's equation, $M - E + e \sin
               (E) = 0$.",
}


@INCOLLECTION
{
   Laws91a,
   AUTHOR    = "Lawson, Charles L.",
   TITLE     = "Automatic Differentiation of Inverse Functions",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "87--94",
   REFERRED  = "[Flan91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Layn91a,
   AUTHOR    = "Layne, J. Daniel",
   TITLE     = "Applying Automatic Differentiation and Self-Validating
                Numerical Methods in Satellite Simulations",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "211--217",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Lewi85a,
   AUTHOR    = "J. M. Lewis 
                and J. C. Derber",
   TITLE     = "The Use of Adjoint Equations to Solve a Variational 
                Adjustment Problem with Advective Constraints",
   JOURNAL   = "Tellus",
   VOLUME    = "37A",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1985",
   PAGES     = "309--322",
   REFERRED  = "[Navo91a].",
   COMMENT   = "Talagrand gives pages as 97--110.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Liep90a,
   AUTHOR    = "Liepel, M.
                and Schittkowski, K.",
   TITLE     = "{PCOMP}: {A} {FORTRAN} Code for Automatic Differentiation",
   INSTITUTION = "DFG Schwerpunktprogramm Anwendungsbezogene Optimierung
                und Optimale Steuerung, Mathematisches Institut, 
                Universit{\"a}t Bayreuth",
   YEAR      = "1990",
   TYPE      = "Report",
   NUMBER    = "No. 254",
   ADDRESS   = "D-8580 Bayreuth, Germany",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Lill70a,
   AUTHOR    = "Lill, S. A.",
   TITLE     = "Algorithm 46:  {A} modified {D}avidon method for 
                finding the minimum of a function using difference 
                approximation for derivatives",
   JOURNAL   = "The Computer J.",
   VOLUME    = "13",
   NUMBER    = "",
   YEAR      = "1970",
   PAGES     = "111--113",
   NOTE      = "14 (170), p. 106",
   REFERRED  = "[Garc91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MISC
{
   Lind91a,
   AUTHOR    = "Lindell, R.",
   TITLE     = "Response to electronic mail survey",
   HOWPUBLISHED = "Personal communication",
   MONTH     = "March",
   YEAR      = "1991",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Linn76a,
   AUTHOR    = "Linnainmaa, S.",
   TITLE     = "Taylor Expansion of the Accumulated Rounding Error",
   JOURNAL   = "BIT (Nordisk Tidskrift for Informationsbehandling)",
   VOLUME    = "16",
   NUMBER    = "1",
   YEAR      = "1976",
   PAGES     = "146--160",
   REFERRED  = "[Bisc91f]; [Char91a]; [Irim91a]; [Kubo91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Lion71a,
   AUTHOR    = "Lions, J. L.",
   TITLE     = "Optimal Control of Systems Governed by Partial 
                Differential Equations",
   PUBLISHER = "Springer Verlag",
   SERIES    = "",
   ADDRESS   = "Berlin",
   YEAR      = "1971",
   REFERRED  = "[Tala91a].",
   NOTE      = "(Translation from the French edition, Dunod, Paris, 1969).",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Lisk90a,
   author    = "R. Liska 
                and L. Drska",
   title     = "{FIDE}: {A} {REDUCE} package for automation of finite 
                difference method for solving {PDE}",
   booktitle = "Proceedings of the 1990 International Symposium on 
                Symbolic and Algebraic Computation",
   year      = "1990",
   editor    = "Shunro Watanabe 
                and Morio Nagata",
   pages     = "169--176",
   publisher = "Addison-Wesley",
   ADDRESS   = "Reading, Mass.",
   REFERRED  = "[Char91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Liud88a,
   AUTHOR    = "D. C. Liu 
                and J. Nocedal",
   TITLE     = "On the Limited Memory {BFGS} Method for 
                Large Scale Optimization",
   INSTITUTION = "Northwestern University",
   MONTH     = "",
   YEAR      = "1988",
   TYPE      = "Technical Report",
   NUMBER    = "NAM 03",
   ADDRESS   = "Evanston, Ill.",
   REFERRED  = "[Navo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Lohn87a,
   AUTHOR    = "Lohner, Rudolph J.",
   TITLE     = "Enclosing the solutions of ordinary initial and boundary 
                value problems",
   BOOKTITLE = "Computer Arithmetic: {S}cientific Computation and
                Programming Languages",
   YEAR      = "1987",
   EDITOR    = "Kaucher, Edgar W. 
                and Kulisch, Ulrich W.  
                and Ullrich, Christian",
   PUBLISHER = "Wiley-Teubner Series in Computer Science",
   ADDRESS   = "Stuttgart",
   PAGES     = "255--286",
   REFERRED  = "[Layn91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Lore81a,
   AUTHOR    = "Lorenc, A. C.",
   TITLE     = "A global three-dimensional multivariate statistical 
                interpolation scheme",
   JOURNAL   = "Monthly Weather Review",
   VOLUME    = "109",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1981",
   PAGES     = "701--721",
   REFERRED  = "[Tala91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Lore88a,
   AUTHOR    = "Lorenc, A. C.",
   TITLE     = "Optimal nonlinear objective analysis",
   JOURNAL   = "Q. J. R. Meteorol. Soc.",
   VOLUME    = "114",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1988",
   PAGES     = "205--240",
   REFERRED  = "[Tala91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Maan89a,
   AUTHOR    = "Maany, Z.",
   TITLE     = "{A}da Automatic Differentiation Package for the
                Optimization of Functions of Many Variables",
   TYPE      = "Technical Report",
   NUMBER    = "NOC TR209",
   INSTITUTION = "The Numerical Optimisation Center, Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   MONTH     = "July",
   YEAR      = "1989",
   PAGES     = "",
   REFERRED  = "[Dixo89b].",
   COMMENT   = "",
   KEYWORDS  = "optimization",
   ABSTRACT  = "",
}


@ARTICLE
{
   Maan89b,
   AUTHOR    = "Maany, Z. A.",
   TITLE     = "{FORTRAN} Automatic Differentiation Package for the
                Optimization of Functions of Many Variables",
   JOURNAL   = "",
   VOLUME    = "",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "to appear",
   PAGES     = "",
   REFERRED  = "[Dixo89b].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Marc74a,
   AUTHOR    = "Marchuk, G. I.",
   TITLE     = "Numerical Solution of the Problems of the Dynamics of 
                the Atmosphere and Ocean",
   PUBLISHER = "Gidrometeoizdat",
   SERIES    = "",
   ADDRESS   = "Leningrad",
   YEAR      = "1974",
   REFERRED  = "[Navo91a]; [Tala91a].",
   NOTE      = "(In Russian).",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Maso53a,
   AUTHOR    = "Mason, S. J.",
   TITLE     = "Feedback theory --- {S}ome properties of signal flow graphs",
   JOURNAL   = "Proceedings of IRE",
   VOLUME    = "41",
   NUMBER    = "",
   YEAR      = "1953",
   PAGES     = "1144--1156",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Mats70a,
   AUTHOR    = "H.~Matsuda 
                and H.~Wollnik",
   TITLE     = "The influence of an inhomogeneous magnetic fringing 
                field on the trajectories of charged particles in a 
                third order approximation",
   JOURNAL   = "Nuclear Instruments and Methods",
   VOLUME    = "77",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1970",
   PAGES     = "40 +",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Mats70b,
   AUTHOR    = "H.~Matsuda 
                and H.~Wollnik",
   TITLE     = "Third order transfer matrices of the fringing field of an
                inhomogeneous magnet",
   JOURNAL   = "Nuclear Instruments and Methods",
   VOLUME    = "77",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1970",
   PAGES     = "283 +",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Mats72a,
   AUTHOR    = "T.~Matsuo  
                and H.~Matsuda 
                and H.~Wollnik",
   TITLE     = "Particle trajectories in a toroidal condenser in a third order
                approximation",
   JOURNAL   = "Nuclear Instruments and Methods",
   VOLUME    = "103",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1972",
   PAGES     = "515 +",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Math89a,
   AUTHOR    = "MATH",
   TITLE     = "{MATH77}, {R}elease 3.0, {A} Library of Mathematical 
                Subprograms for {FORTRAN} 77",
   INSTITUTION = "Jet Propulsion Laboratory",
   ADDRESS   = "Pasadena, Calif.",
   MONTH     = "May",
   YEAR      = "1989",
   TYPE      = "Internal Document",
   NUMBER    = "D--134, Rev. B",
   REFERRED  = "[Jued91a]; [Laws91a].",
   NOTE      = "Also available as Program No. NPO--18120 from COSMIC
                (Computer Software Management and Information  Center),
                The University of Georgia, Athens, Georgia",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Mati86a,
   AUTHOR    = "Matiyasevich, {\Yu}. V.",
   TITLE     = "Veshchestvennye chisla i {{\`E}{VM}}",
   JOURNAL   = "Kibernetika i Vychislitel'naya Tekhnika",
   VOLUME    = "2",
   NUMBER    = "",
   YEAR      = "1986",
   PAGES     = "104--133",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Mazo91a,
   AUTHOR    = "Mazourik, Vladimir",
   TITLE     = "Integration of Automatic Differentiation into 
                a Numerical Library for {PC}'s",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "286--293",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Mazu90a,
   author    = "S. I. Mazurik 
                and E. V. Vorozhtsov",
   title     = "Symbolic-numeric computations in the stability 
                analyzes of difference schemes",
   booktitle = "Proceedings of the 1990 International Symposium on 
                Symbolic and Algebraic Computation",
   year      = "1990",
   editor    = "Shunro Watanabe 
                and Morio Nagata",
   pages     = "177--184",
   publisher = "Addison-Wesley",
   ADDRESS   = "Reading, Mass.",
   REFERRED  = "[Char91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   McCo83a,
   AUTHOR    = "McCormick, G.P.",
   TITLE     = "Nonlinear Programming",
   YEAR      = "1983",
   PUBLISHER = "John Wiley and Sons",
   SERIES    = "",
   ADDRESS   = "New York",
   REFERRED  = "[Fisc91b].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   McCu43a,
   AUTHOR    = "McCulloch, W.S.
                and Pitts, W.",
   TITLE     = "A logical calculus of ideas immanent in nervous activity",
   JOURNAL   = "Bulletin of Mathematical Biophysics",
   VOLUME    = "5",
   NUMBER    = "",
   YEAR      = "1943",
   PAGES     = "115--133",
   REFERRED  = "[Saar91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   McCu69a,
   AUTHOR    = "McCully, J. D.",
   TITLE     = "The {Q} Approach to Problem Solving",
   BOOKTITLE = "Proceedings of FJCC 69",
   PUBLISHER = "AFIPS",
   YEAR      = "1969",
   PAGES     = "691--699",
   REFERRED  = "[Jued91a]; [Tham91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Mich90a,
   AUTHOR    = "Michelotti, Leo",
   TITLE     = "{MXYZPTLK}: {A} Practical, User-Friendly {C++} 
                Implementation of Differential Algebra: {U}ser's Guide",
   INSTITUTION = "Fermi National Accelerator Laboratory",
   MONTH     = "January",
   YEAR      = "1990",
   TYPE      = "Technical Memorandum",
   NUMBER    = "FN--535",
   ADDRESS   = "Batavia, Ill.",
   REFERRED  = "[Jued91a]; [Mich91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Mich91a,
   AUTHOR    = "Michelotti, Leo",
   TITLE     = "{MXYZPTLK}: {A} {C}++ Hacker's Implementation of 
                Automatic Differentiation",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "218--227",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Mill75a,
   AUTHOR    = "W. Miller",
   TITLE     = "Software for roundoff analysis",
   JOURNAL   = "ACM Trans. Math. Software",
   YEAR      = "1975",
   VOLUME    = "1",
   NUMBER    = "2",
   PAGES     = "108--128",
   REFERRED  = "[Char91a].",
   COMMENT   = "Char -- good paper.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Mill88a,
   AUTHOR    = "G. L. Miller 
                and V. Ramachandran 
                and E. Kaltofen",
   TITLE     = "Efficient parallel evaluation of straight-line code and 
                arithmetic circuits",
   JOURNAL   = "SIAM J. Comp.",
   VOLUME    = "17",
   NUMBER    = "",
   YEAR      = "1988",
   PAGES     = "687-695",
   REFERRED  = "[Grie91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Mill75b,
   AUTHOR    = "W. Miller",
   TITLE     = "Computer search for numerical stability",
   JOURNAL   = "J. ACM",
   YEAR      = "1975",
   VOLUME    = "22",
   NUMBER    = "",
   PAGES     = "512--521",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Mill76b,
   AUTHOR    = "W. Miller",
   TITLE     = "Roundoff analysis by direct comparison of two algorithms",
   JOURNAL   = "{SIAM J. Numerical Analysis}",
   YEAR      = "1976",
   VOLUME    = "13",
   NUMBER    = "",
   PAGES     = "282--292",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Mill80a,
   AUTHOR    = "Miller, W.
                and Wrathall, C.",
   TITLE     = "Software for Roundoff Analysis of Matrix Algorithms",
   PUBLISHER = "Academic Press",
   ADDRESS   = "New York",
   YEAR      = "1980",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; differentiation arithmetic.",
   ABSTRACT  = "Chapter 3 of the book describes the concept of a directed
                graph.  It uses the calculation of first order partial
                derivatives as an example.  Roundoff error results are given.",
}


@BOOK
{
   Mins88a,
   AUTHOR    = "Minsky, M.
                and Papert, S.",
   TITLE     = "Perceptrons",
   EDITION   = "rev.",
   PUBLISHER = "MIT Press",
   SERIES    = "",
   ADDRESS   = "Cambridge, Mass.",
   YEAR      = "1988",
   REFERRED  = "[Saar91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MISC
{
   Mona91a,
   AUTHOR    = "Monagan, Mike",
   TITLE     = "Response to electronic mail survey",
   HOWPUBLISHED = "Personal communication",
   MONTH     = "March",
   YEAR      = "1991",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MISC
{
   Mona91b,
   AUTHOR    = "Monagan, Mike",
   TITLE     = "Regarding changes to 
                \protect{\tt optimize} command for future versions 
                of {MAPLE}",
   HOWPUBLISHED = "Personal communication",
   MONTH     = "",
   YEAR      = "1991",
   REFERRED  = "[Char91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Moor66a,
   AUTHOR    = "Moore, Ramon E.",
   TITLE     = "Interval Analysis",
   PUBLISHER = "Prentice-Hall",
   YEAR      = "1966",
   ADDRESS   = "Englewood Cliffs, N.J.",
   REFERRED  = "[Garl85a] \# 967, 969; [Bart70a]; [Chan74a];
                [Corl82a]; [Corl87a]; [Corl88a]; [Corl91a]; [Gray67a]; 
                [Gray74a]; [Hali83a]; [Iri84a]; [Kuba72a]; [Moor79a]; 
                [Rall80a]; [Rall81a];
                [Yohe79a].",
   COMMENT   = "German translation: {\sl Intervallanalyse,\/} translated by
                D. Pfaffenzeller, R. Oldenburg, M{\"u}nchen, 1968.",
   KEYWORDS  = "boundary value problems; wrapping effect; coordinate
                transformation; Taylor coefficients.",
   ABSTRACT  = "Chapter ten of this book discusses the machine generation
                of Taylor coefficients.  Basic recursion relations are
                presented.",
}


@BOOK
{
   Moor79a,
   AUTHOR    = "Moore, Ramon E.",
   TITLE     = "Methods and Applications of Interval Analysis",
   PUBLISHER = "SIAM",
   YEAR      = "1979",
   ADDRESS   = "Philadelphia, Penn.",
   REFERRED  = "[Corl87a]; [Corl91a]; 
                 [Garl85a] \#980; [Aber88a];
                 [Corl88a]; [Layn91a]; [Neid89a];
                 [Rall80a]; [Rall81a]; [Rall85a]; 
                 [Rall91a].",
   COMMENT   = "",
   KEYWORDS  = "operator equations; Taylor series; wrapping effect; boundary
                value problems.",
   ABSTRACT  = "Chapter 3 of this book discusses differation arithmetic as a
                recursive iteration.  That is, for calculating Taylor
                coefficients.",
}


@TECHREPORT
{
   Moor79b,
   AUTHOR    = "Moore, R. E.
                and others",
   TITLE     = "{AIRDOS-EPA}:  {A} Computerized Methodology for
                Estimating Environmental Concentrations and Dose to Man from
                Airborne Releases of Radionuclides",
   INSTITUTION = "Oak Ridge National Laboratory",
   YEAR      = "1979",
   TYPE      = "Technical Report",
   NUMBER    = "ORNL-5532",
   ADDRESS   = "Oak Ridge, Tenn.",
   REFERRED  = "[Horw91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   More90a,
   AUTHOR    = "Mor\'{e}, Jorge J.",
   TITLE     = "On the Performance of Algorithms for Large-Scale
                Bound Constrained Problems",
   BOOKTITLE = "Large-Scale Numerical Optimization",
   EDITOR    = "T. F. Coleman
                and Y. Li",
   YEAR      = "1991",
   PUBLISHER = "SIAM",
   PAGES     = "32--45",
   REFERRED  = "[Bisc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   More80a,
   AUTHOR    = "Mor\'{e}, Jorge J.
                and Garbow, B. S.
                and Hillstrom, K. E.",
   TITLE     = "Implementation guide for {MINPACK}--1",
   INSTITUTION = "Mathematics and Computer Sciences Division, 
                Argonne National Laboratory",
   YEAR      = "1980",
   TYPE      = "Technical Report",
   NUMBER    = "ANL--80--68",
   ADDRESS   = "Argonne, Ill.",
   MONTH     = "",
   REFERRED  = "[Bisc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   More80b,
   AUTHOR    = "Mor\'{e}, Jorge J.
                and Garbow, B. S.
                and Hillstrom, K. E.",
   TITLE     = "User guide for {MINPACK}--1",
   INSTITUTION = "Mathematics and Computer Sciences Division, 
                Argonne National Laboratory",
   YEAR      = "1980",
   TYPE      = "Technical Report",
   NUMBER    = "ANL--80--74",
   ADDRESS   = "Argonne, Ill.",
   MONTH     = "",
   REFERRED  = "[Bisc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   More81a,
   AUTHOR    = "Mor\'{e}, Jorge J.
                and Garbow, Burton S.
                and Hillstrom, Kenneth E.",
   TITLE     = "Testing unconstrained optimization software",
   JOURNAL   = "ACM Trans. Math. Software",
   VOLUME    = "7",
   NUMBER    = "1",
   YEAR      = "1981",
   PAGES     = "17--41",
   REFERRED  = "[Soul91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   More81b,
   AUTHOR    = "Mor\'{e}, Jorge J.
                and Garbow, Burton S.
                and Hillstrom, Kenneth E.",
   TITLE     = "Algorithm 566.  {FORTRAN} Subroutines for
                Testing Unconstrained Optimization Software",
   JOURNAL   = "ACM Trans. Math. Software",
   VOLUME    = "7",
   NUMBER    = "1",
   YEAR      = "1981",
   PAGES     = "136--140",
   REFERRED  = "[Gayd91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Morg84a,
   AUTHOR    = "Morgenstern, J.",
   TITLE     = "How to compute fast a function and all its derivatives.  
                {A} variation on the theorem of {B}aur-{S}trassen",
   INSTITUTION = "Laboratoire CNRS 168, Universit\'{e} de Nice",
   MONTH     = "",
   YEAR      = "1984",
   TYPE      = "Report",
   NUMBER    = "No. 49",
   ADDRESS   = "Nice, France",
   REFERRED  = "[Tala91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Mori90a,
   AUTHOR    = "Moriguti, S.
                and Iri, Masao
                and Kabaya-Imai, K.",
   TITLE     = "On asymptotic properties of the eigenfunctions 
                of a linear operator",
   JOURNAL   = "Japan J. Applied Mathematics",
   VOLUME    = "7",
   NUMBER    = "",
   YEAR      = "1990",
   PAGES     = "203--229",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Mort74a,
   AUTHOR    = "Morton, H. S. 
                and Jenkins, J. L.
                and Blanton, J. N.",
   TITLE     = "Analytical solutions for {E}uler parameters",
   JOURNAL   = "Celestial Mechanics",
   VOLUME    = "10",
   NUMBER    = "",
   YEAR      = "1974",
   PAGES     = "287--301",
   REFERRED  = "[Layn91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Mung90a,
   AUTHOR    = "Munger, Fredrick S.",
   TITLE     = "Applications of Definor Algebra to Ordinary Differential
                Equations",
   PUBLISHER = "AfterMath Press",
   SERIES    = "",
   ADDRESS   = "",
   YEAR      = "1990",
   REFERRED  = "",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Muro87a,
   AUTHOR    = "Murota, K.",
   TITLE     = "Systems Analysis by Graphs and Matroids 
                --- {S}tructural Solvability and Controllability",
   PUBLISHER = "Springer Verlag",
   SERIES    = "",
   ADDRESS   = "",
   YEAR      = "1987",
   REFERRED  = "[Irim91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Muro87b,
   AUTHOR    = "Murota, K.",
   TITLE     = "Menger-decomposition of a graph and its application 
                to the structural analysis of a large-scale
                system of equations",
   JOURNAL   = "Discrete Applied Mathematics",
   VOLUME    = "17",
   NUMBER    = "",
   YEAR      = "1987",
   PAGES     = "",
   REFERRED  = "[Grie91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Muro89a,
   AUTHOR    = "Murota, K.
                and Kubota, Koichi",
   TITLE     = "On Elimination of Intermediate Variables in Fast 
                Automatic Differentiation",
   JOURNAL   = "Transactions of Information Processing Society of Japan",
   VOLUME    = "30",
   NUMBER    = "",
   YEAR      = "1989",
   PAGES     = "536--539",
   REFERRED  = "[Kubo91a].",
   NOTE      = "(In Japanese).",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Murt81a,
   AUTHOR    = "Murtagh, B. A.",
   TITLE     = "Advanced Linear Programming: {C}omputation and Practice",
   PUBLISHER = "McGraw-Hill",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1981",
   REFERRED  = "[Gayd91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Murt78a,
   AUTHOR    = "B. A. Murtagh 
                and M. A. Saunders",
   TITLE     = "Large-Scale Linearly Constrained Optimization",
   JOURNAL   = "Math. Programming",
   VOLUME    = "14",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1978",
   PAGES     = "41--72",
   REFERRED  = "[Gayd91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Murt82a,
   AUTHOR    = "B. A. Murtagh 
                and M. A. Saunders",
   TITLE     = "A Projected {L}agrangian Algorithm and Its Implementation
                for Sparse Nonlinear Constraints",
   JOURNAL   = "Math. Programming Study",
   VOLUME    = "16",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1982",
   PAGES     = "84--117",
   REFERRED  = "[Gayd91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Murt87a,
   AUTHOR    = "B. A. Murtagh 
                and M. A. Saunders",
   TITLE     = "{MINOS} 5.1 User's Guide",
   INSTITUTION = "Systems Optimization Laboratory, Stanford University",
   MONTH     = "",
   YEAR      = "1987",
   TYPE      = "Technical Report",
   NUMBER    = "SOL 83-20R",
   ADDRESS   = "Stanford, Calif.",
   REFERRED  = "[Gayd91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@phdthesis
{
   Mutr91a,
   AUTHOR    = "Mark P.W. Mutrie",
   TITLE     = "Towards a Symbolic System for Floating-Point ErrorAnalysis",
   SCHOOL    = "University of Waterloo",
   ADDRESS   = "Waterloo, Canada",
   YEAR      = "1991",
   REFERRED  = "[Char91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Navo79a,
   AUTHOR    = "Navon, I. Michael
                and Muller, U.",
   TITLE     = "{FESW} --- {A} finite-element {F}ortran {IV}
                program for solving the shallow water equations",
   JOURNAL   = "Advances in Engineering Software",
   YEAR      = "1970",
   VOLUME    = "1",
   NUMBER    = "",
   PAGES     = "77--84",
   MONTH     = "",
   NOTE      = "",
   REFERRED  = "[Bisc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Navo90a,
   AUTHOR    = "Navon, I. Michael
                and Zou, Xiaolei 
                and Johnson, K. 
                and Derber, J.
                and Sela, J.",
   TITLE     = "Variational Data Assimilation with an Adiabatic 
                Version of the {NMC} Spectral Model",
   JOURNAL   = "Monthly Weather Review",
   VOLUME    = "",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1990",
   PAGES     = "",
   REFERRED  = "[Navo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Navo90b,
   AUTHOR    = "Navon, I. Michael
                and Zou, Xiaolei 
                and Johnson, K. 
                and Derber, J.
                and Sela, J.",
   TITLE     = "Variational real-data assimilation with the {N.M.C.} 
               spectral model.  {Part I}: {A}diabatic model tests",
   BOOKTITLE = "Proceedings of the International Symposium on Assimilation
                of Observations in Meteorology and Oceanography, World
                Meteorological Organization, Geneva, Switzerland",
   PUBLISHER = "",
   YEAR      = "1990",
   PAGES     = "341--348",
   REFERRED  = "[Tala91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Navo91a,
   AUTHOR    = "Navon, I. Michael
                and Zou, Xiaolei",
   TITLE     = "Application of the Adjoint Model in Meteorology",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "202--207",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Neid89a,
   AUTHOR    = "Neidinger, Richard D.",
   TITLE     = "Automatic Differentiation and {APL}",
   JOURNAL   = "College Mathematics J.",
   VOLUME    = "20",
   NUMBER    = "3",
   YEAR      = "1989",
   PAGES     = "238--251",
   REFERRED  = "[Flan91a]; [Kalm91a].",
   NOTES     = "Also appeared as Lecture Notes, Davidson College,
                Davidson, N.C., 1987.",
   COMMENT   = "",
   KEYWORDS  = "differentiation arithmetic; APL; computer program.",
   ABSTRACT  = "The lecture notes discuss implementing differentiation
                arithmetic in APL.  APL programs which implement the basic
                ideas of differentiation arithmetic are given.  Pascal's
                triangle is a standard feature of APL which allows the binomial
                coefficients required to be found using a table lookup.",
}


@ARTICLE
{
   Neid89b,
   AUTHOR    = "Neidinger, Richard D.",
   TITLE     = "An {APL} Approach to Differential Calculus Yields a
                Powerful Tool",
   JOURNAL   = "APL89 Conference Proceedings, APL Quote Quad",
   VOLUME    = "19",
   NUMBER    = "",
   YEAR      = "1989",
   PAGES     = "285--288",
   REFERRED  = "",
   NOTES     = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Neid90a,
   AUTHOR    = "Neidinger, Richard D.",
   TITLE     = "An Efficient Method for the Numerical
                Evaluation of Partial Derivatives of Arbitrary Order",
   TYPE      = "Preprint",
   INSTITUTION = "Davidson College",
   ADDRESS   = "Davidson, N.C.",
   YEAR      = "1990",
   REFERRED  = "[Jued91a]; [Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = ""
}


@ARTICLE
{
   Neid92a,
   AUTHOR    = "Neidinger, Richard D.",
   TITLE     = "An Efficient Method for the Numerical
                Evaluation of Partial Derivatives of Arbitrary Order",
   JOURNAL   = "ACM Trans. Math. Software",
   VOLUME    = "18",
   NUMBER    = "2",
   YEAR      = "1992",
   MONTH     = "June",
   PAGES     = "159--173",
   REFERRED  = "",
   NOTES     = "Also appeared as Preprint, Davidson College,
                Davidson, N.C., 1990.",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = ""
}


@ARTICLE
{
   Neid92b,
   AUTHOR    = "Neidinger, Richard D.",
   TITLE     = "Differential Equations are Recurrence Relations in {APL} ",
   JOURNAL   = "APL92 Conference Proceedings, APL Quote Quad",
   VOLUME    = "",
   NUMBER    = "",
   YEAR      = "to appear",
   PAGES     = "",
   REFERRED  = "",
   NOTES     = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Nged79a,
   AUTHOR    = "Edward W. Ng",
   TITLE     = "Symbolic-numeric interface:  {A} review",
   BOOKTITLE = "{EUROSAM 79, Colloque International sur les M\'{e}thodes de
                Calcul Symbolique et Alg\'{e}brique}",
   YEAR      = "1979",
   EDITOR    = "Edward W. Ng",
   PAGES     = "330--345",
   ORGANIZATION = "{EUROSAM, Marseille, France}",
   PUBLISHER = "Springer Verlag",
   ADDRESS   = "New York",
   REFERRED  = "[Char91a].",
   COMMENT   = "Char -- Summary of various applications.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Nged79b,
   AUTHOR    = "E. Ng 
                and Bruce W. Char",
   TITLE     = "Gradient and {Jacobian} computation for numerical 
                applications",
   BOOKTITLE = "Proceedings of the 1979 Macsyma User's Conference",
   YEAR      = "1979",
   EDITOR    = "V. Ellen Golden",
   PAGES     = "604--621",
   ORGANIZATION = "{NASA, Washington, D.C.}",
   MONTH     = "June",
   REFERRED  = "[Char91a].",
   COMMENT   = "Char -- Optimization techniques.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Nije78a,
   AUTHOR    = "Nijenhuis, A. 
                and Wilf, H. S.",
   TITLE     = "Combinatorial Algorithms",
   EDITION   = "2nd",
   PUBLISHER = "Academic Press",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1978",
   REFERRED  = "[Flan91a]; [Laws91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   NOC76a,
   AUTHOR    = "N.O.C.",
   TITLE     = "{OPTIMA} - {R}outines for Optimisation Problems",
   TYPE      = "{T}echnical {R}eport",
   NUMBER    = "",
   INSTITUTION = "The Numerical Optimisation Center, Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   YEAR      = "1976",
   REFERRED  = "[Garc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Noce80a,
   AUTHOR    = "Nocedal, J.",
   TITLE     = "Updating Quasi-{N}ewton Matrices with Limited Storage",
   JOURNAL   = "Mathematics of Computation",
   VOLUME    = "35",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1980",
   PAGES     = "773--782",
   REFERRED  = "[Navo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MastersThesis
{
   Nola53a,
   author    = "Nolan, J. F.",
   title     = "Analytical Differentiation on a Digital Computer",
   school    = "Massachusetts Institute of Technology",
   year      = "1953",
   month     = "May",
   REFERRED  = "[Char91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Oblo78a,
   AUTHOR    = "Oblow, E. M.",
   TITLE     = "Sensitivity Theory for Reactor Thermal-Hydraulics Problems",
   JOURNAL   = "Nucl. Sci. Eng.",
   VOLUME    = "68",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1978",
   PAGES     = "322",
   REFERRED  = "[Worl91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Oblo83a,
   AUTHOR    = "Oblow, E. M.",
   TITLE     = "An Automated Procedure for Sensitivity Analysis 
                Using Computer Calculus",
   INSTITUTION = "Union Carbide Corp., Nucl. Div., 
                Oak Ridge National Laboratory",
   ADDRESS   = "Oak Ridge, Tenn.",
   YEAR      = "1983",
   TYPE      = "",
   NUMBER    = "ORNL/TM-8776",
   REFERRED  = "[Horw91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Oblo83b,
   AUTHOR    = "Oblow, E. M.",
   TITLE     = "{GRESS}: {G}radient-Enhanced Software System. 
                {V}ersion {B}",
   INSTITUTION = "Union Carbide Corp., Nucl. Div., 
                Oak Ridge National Laboratory",
   ADDRESS   = "Oak Ridge, Tenn.",
   YEAR      = "1983",
   TYPE      = "{T}ech. {R}eport",
   NUMBER    = "ORNL/TM-8339",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Oblo85a,
   AUTHOR    = "Oblow, E. M.",
   TITLE     = "{GRESS}: {G}radient-enhanced software system. {V}ersion {D}
                User's guide",
   TYPE      = "{T}ech. {R}eport",
   INSTITUTION = "Oak Ridge National Laboratory",
   ADDRESS   = "Oak Ridge, Tenn.",
   YEAR      = "1985",
   REFERRED  = "",
   COMMENT   = "This is a user's guide to a package which incorporates
                differentiation arithmetic.",
   KEYWORDS  = "Differentiation arithmetic; computer program; sensitivity
                analysis; preprocessor.",
   ABSTRACT  = "This describes a Fortran precompiler which takes as input
                Fortran programs.  These are then differentiated using
                differentiation arithmetic techniques.  The output is a
                Fortran subroutine which will calculate the value of the
                Jacobian of a function without using finite differencing.
                The packages main application is in the area of sensitivity
                analysis.",
}


@ARTICLE
{
   Oblo86a,
   AUTHOR    = "Oblow, E. M. 
                and Pin, F. G.
                and Wright, R. Q.",
   TITLE     = "Sensitivity Analysis Using Computer Calculus: 
                {A} Nuclear Waste Application",
   JOURNAL   = "Nucl. Sci. Eng.",
   VOLUME    = "94",
   NUMBER    = "46",
   YEAR      = "1986",
   PAGES     = "",
   REFERRED  = "[Horw91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   ONei71a,
   AUTHOR    = "O'Neill, R.",
   TITLE     = "Algorithm {AS47} - {F}unction minimization using a 
                simplex procedure",
   JOURNAL   = "Applied Statistics",
   VOLUME    = "20, 23, 25",
   NUMBER    = "",
   YEAR      = "1971",
   PAGES     = "338--346, 250--252, 97",
   REFERRED  = "[Garc91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Ostr71a,
   AUTHOR    = "Ostrovskii, G. M.
                and Wolin, {\Ju}. M.
                and Borisov, W. W.",
   TITLE     = "{\"U}ber die {B}erechnung von {A}bleitungen",
   JOURNAL    = "Wissenschaftliche Zeitschrift der Technischen
		    Hochschule f{\"u}r Chemie, Leuna-Merseburg",
   VOLUME    = "13",
   NUMBER    = "4",
   MONTH     = "",
   YEAR      = "1971",
   PAGES     = "382--384",
   REFERRED  = "[Voli85a].",
   COMMENT   = "This is a desciption of a program for automatic derivative
                computation.",
   KEYWORDS  = "differentiation arithmetic; back method; computer program.",
   ABSTRACT  = "",
}


@ARTICLE
{
   Pant88a,
   AUTHOR    = "Pantelides, C. C.",
   TITLE     = "{SPEEDUP} Recent Advances in Process Simulation",
   JOURNAL   = "Comput. Chem. Engin.",
   VOLUME    = "12",
   NUMBER    = "",
   YEAR      = "1988",
   PAGES     = "745--755",
   REFERRED  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Park90a,
   AUTHOR    = "Parkhurst, S. C.",
   TITLE     = "The Evaluation of Exact Numerical {J}acobians using 
                Automatic Differentiation",
   TYPE      = "Technical Report",
   NUMBER    = "NOC TR224",
   INSTITUTION = "The Numerical Optimisation Center, Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   MONTH     = "December",
   YEAR      = "1990",
   REFERRED  = "[Dixo91a].",
   COMMENT   = "Presented at The Eleventh Conference on Differential 
                Equations, Dundee University, July 1990.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Parl80a,
   AUTHOR    = "Parlett, P.",
   TITLE     = "The Symmetric Eigenvalue Problem",
   PUBLISHER = "Prentice-Hall",
   SERIES    = "Series in Computational Mathematics",
   ADDRESS   = "Englewood Cliffs, N.J.",
   YEAR      = "1980",
   REFERRED  = "[Tala91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Pask67a,
   AUTHOR    = "Paskhin, {\Ye}. N.",
   TITLE     = "Analytic function differentiation by computer",
   JOURNAL   = "Computer Methods and Programming",
   VOLUME    = "9",
   YEAR      = "1967",
   PAGES     = "",
   REFERRED  = "[Voli85a].",
   NOTE      = "(In Russian).",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; symbolic algebra; program transformation.",
   ABSTRACT  = "",
}
 

@ARTICLE
{
   Pave85a,
   AUTHOR    = "Pavelle, Richard
                and Wang, Paul S.",
   TITLE     = "{MACSYMA} from {F} to {G}",
   JOURNAL   = "J. Symbolic Computation",
   VOLUME    = "1",
   NUMBER    = "1",
   MONTH     = "March",
   YEAR      = "1985",
   PAGES     = "69--100",
   REFERRED  = "[Char91a]; [Gold91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Peac55a,
   AUTHOR    = "D. W. Peaceman 
                and H. H. {Rachford, Jr.}",
   TITLE     = "The Numerical Solution of Parabolic and 
                Elliptic Differential Equations",
   JOURNAL   = "J. SIAM",
   VOLUME    = "3",
   NUMBER    = "1",
   MONTH     = "",
   YEAR      = "1955",
   PAGES     = "28--41",
   REFERRED  = "[Shah91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Pene76a,
   AUTHOR    = "V. V. Penenko 
                and N. N. Obraztsov",
   TITLE     = "A Variational Initialization Method 
                for the Fields of the Meteorological Elements",
   JOURNAL   = "Meteorol. Gidrol. (Soviet Meteorol. Hydrol.)",
   VOLUME    = "11",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1976",
   PAGES     = "1--11",
   REFERRED  = "[Navo91a].",
   NOTE      = "(English translation).",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Pfei80a,
   AUTHOR    = "Pfeiffer, F. W.",
   TITLE     = "Some Advances Related to Nonlinear Programming",
   JOURNAL   = "SIGMAP Bulletin",
   VOLUME    = "",
   NUMBER    = "",
   YEAR      = "1980",
   MONTH     = "January",
   PAGES     = "1--7",
   REFERRED  = "[Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = ""
}


@ARTICLE
{
   Pfei87a,
   AUTHOR    = "Pfeiffer, F. W.",
   TITLE     = "Automatic differentiation in {PROSE}",
   JOURNAL   = "ACM SIGNUM Newsletter",
   VOLUME    = "22",
   NUMBER    = "1",
   YEAR      = "1987",
   PAGES     = "1--8",
   REFERRED  = "[Jued91a]; [Tham91a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; differentiation arithmetic; program
               transformation.",
   ABSTRACT  = "A programming language is presented in which has the feature
                that first and second order partial derivatives of a
                function can be calculated using differentiation arithmetic.
                The language syntax allows the user to specify which
                variables each function is required to be differentiated
                with respect to.  Model examples are provided."
}


@INCOLLECTION
{
   Plas90a,
   AUTHOR    = "Plassmann, Paul E.",
   TITLE     = "Sparse {J}acobian estimation and factorization on a
                multiprocessor",
   BOOKTITLE = "Large-Scale Optimization",
   YEAR      = "1990",
   EDITOR    = "Coleman, T. F.
                and Li, Y.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "152--179",
   REFERRED  = "[Bisc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Pohl89a,
   AUTHOR    = "Pohl, Ira",
   TITLE     = "{C}++ for Programmers",
   PUBLISHER = "Benjamin/Cummings",
   SERIES    = "",
   ADDRESS   = "Redwood City, Calif.",
   YEAR      = "1989",
   REFERRED  = "[Kalm91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Pres86a,
   AUTHOR    = "Press, W. H.
                and Flannery, B. P.
                and Teukolsky, S. A.
                and Vetterling, W. T.",
   TITLE     = "Numerical Recipes: {T}he Art of Scientific Computing",
   PUBLISHER = "Cambridge University Press",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1986",
   REFERRED  = "[Layn91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@PHDTHESIS
{
   Pric87a,
   AUTHOR    = "Price, Richard C.",
   TITLE     = "Sparse Matrix Optimisation using Automatic Differentiation",
   SCHOOL    = "Hatfield Polytechnic",
   ADDRESS   = "Hatfield, U.K.",
   YEAR      = "1987",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "differentiation arithmetic; sparse; optimisation.",
   ABSTRACT  = "This thesis considers the problem of finding a minimum of
                a multivariate function with and without constraints.  The
                truncated Newton method is used as the method for finding
                the minima, see [Dixo88a].  In the constrained case, the
                Di Pillo Grippo penalty function is used.  As these methods
                require first and second order tensors, differentiation
                arithmetic is used.  A modification is made to the basic
                method described in [Rall81a] which allows only vector
                storage to be used.  Various modifications of the method are
                applied to real-life problems, and comparisons are given."
}


@TECHREPORT
{
   Pryc87a,
   AUTHOR    = "Pryce, John D. 
                and Davis, Paul H.",
   TITLE     = "A New Implementation of Automatic Differentiation for 
                Use with Numerical Software",
   INSTITUTION = "Mathematics Department, Bristol University",
   MONTH     = "",
   YEAR      = "1987",
   TYPE      = "Technical Report",
   NUMBER    = "TR AM-87-11",
   ADDRESS   = "",
   REFERRED  = "[Dixo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Pryc91a,
   AUTHOR    = "Pryce, John D.
                and Stephens, Bruce R.",
   TITLE     = "The {DAPRE} Preprocessor Users' Guide",
   INSTITUTION = "Royal Military College of Science at Shrivenham",
   ADDRESS   = "Shrivenham, U.K.",
   TYPE      = "Technical Report",
   NUMBER    = "ACM--91--3",
   YEAR      = "1991",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MANUAL
{
   PROS77a,
   AUTHOR    = "",
   TITLE     = "{PROSE} -- {A} General Purpose Higher Level Language",
   ORGANIZATION = "Control Data Corporation",
   NOTE      = "Procedure Manual (Pub. No. 84003000 Rev. B), 
                Calculus Operations Manual (Pub. No. 84003200 Rev. A), 
                Calculus Applications Guide (Pub. No. 84000170 Rev. A).",
   ADDRESS   = "",
   YEAR      = "1977",
   REFERRED  = "[Jued91a]; [Tham91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MANUAL
{
   Radi91a,
   AUTHOR    = "{Radiation Shielding}",
   TITLE     = "{GRESS} 1.0, Gradient Enhanced Software System",
   ORGANIZATION = "distributed by 
                Radiation Shielding Information Center, PSR-231",
   ADDRESS   = "",
   YEAR      = "1991",
   REFERRED  = "[Worl91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Rall69a,
   AUTHOR    = "Rall, Louis B.",
   TITLE     = "Computational Solution of Nonlinear Operator
                Equations",
   PUBLISHER = "Wiley",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1969",
   NOTE      = "Reprinted by Krieger, Huntington, N.Y., 1979.",
   REFERRED  = "[Rall81a]; [Rall91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Rall80a,
   AUTHOR    = "Rall, Louis B.",
   TITLE     = "Applications of software for automatic differentiation in
                numerical computation",
   BOOKTITLE = "Fundamentals of Numerical Computation (Computer Oriented
                Numerical Analysis)",
   PUBLISHER = "Springer Verlag",
   ADDRESS   = "Berlin",
   SERIES    = "Computing Supplement No. 2",
   EDITOR    = "Alefeld, G.
                and Grigorieff, R. D.",
   YEAR      = "1980",
   PAGES     = "141--156",
   REFERRED  = "[Garl85a] \# 1238; [Capr81a]; [Carl86a];
                [Corl88a]; [Kubo91a]; [Rall81a]; [Rall84a].",
   COMMENT   = "In [Alef80a].  Also appeared as {\sl MRC Technical Summary
                Report No. 1976,\/} Mathematics Research Center, University
                of Wisconsin - Madison (1979).",
   KEYWORDS  = "automatic differentiation; Taylor series; Lie series.",
   ABSTRACT  = "Rall outlines generation of a code list, adding operations
                to the code list to compute derivatives or partial
                derivatives, and the automatic generation of Taylor series.
                He surveys the work in these areas done at the University of
                Wisconsin roughly between 1960 and 1980.  Automatic
                differentiation can be applied to ordinary differential
                equations for either Taylor series or Lie series solutions.
                The use of automatic differentiation in nonlinear systems,
                nonlinear functionals, analysis of roundoff errors
                (sensitivity analysis), computational validation of
                existence and uniqueness, and quadrature is surveyed.  This
                paper is a good summary of [Rall81a].",
}


@BOOK
{
   Rall81a,
   AUTHOR    = "Rall, Louis B.",
   TITLE     = "Automatic Differentiation: {T}echniques and Applications",
   PUBLISHER = "Springer Verlag",
   YEAR      = "1981",
   VOLUME    = "120",
   SERIES    = "Lecture Notes in Computer Science",
   ADDRESS   = "Berlin",
   REFERRED  = "[Garl85a] \# 1243; [Arbe85a]; [Carl86a];
                [Carl86b]; [Carl86c]; [Chan86a]; [Corl82a]; [Corl87a];
                [Corl88a]; [Corl91a]; [Dixo87a]; 
                [Dixo91a]; [Fisc87a]; [Fisc91b]; [Garc91a]; [Hali83a]; 
                [Hill82a]; [Irim84a]; [Irim91a]; [Jued91a]; [Kagi86a]; 
                [Layn91a]; [Mazo91a]; [Neid89a];
                [Pfei87a]; [Rall84a]; [Rall85a]; [Rall87a]; [Rall91a]; 
                [Tesf91a];
                [Voli85a]; [Wexl87a].",
   COMMENT   = "Contains all the details about how to do automatic
                differentiation and surveys application to ordinary
                differential equations.",
   KEYWORDS  = "automatic differentiation.",
   ABSTRACT  = "Rall gives complete details on algorithms for the generation
                and differentiation of code lists for expressions.
                Recurrence relations for Taylor coefficients are given.
                Applications to ordinary differential equations, quadrature,
                optimization, and other problems are given.",
}


@INCOLLECTION
{
   Rall83a,
   AUTHOR    = "Rall, Louis B.",
   TITLE     = "Differentiation and generation of {T}aylor coefficients in
                {P}ascal-{SC}",
   BOOKTITLE = "A New Approach to Scientific Computation",
   PUBLISHER = "Academic Press",
   ADDRESS   = "New York",
   EDITOR    = "Kulisch, Ulrich W.
                and Miranker, Willard L.",
   YEAR      = "1983",
   PAGES     = "291--309",
   REFERRED  = "CR 8411 0945; [Garl85a] \# 1252; [Carl86a]; [Carl86b];
                [Carl86c]; [Layn91a]; [Pfei87a]; 
                [Rall85a]; [Rall87a]; [Rall91a].",
   COMMENT   = "Also appeared as {\sl MRC Technical Summary
                Report No. 2452,\/} Mathematics Research Center, University
                of Wisconsin - Madison (1982).",
   KEYWORDS  = "differentiation arithmetic.",
   ABSTRACT  = "",
}


@ARTICLE
{
   Rall83b,
   AUTHOR    = "Rall, Louis B.",
   TITLE     = "Mean value and {T}aylor forms in interval analysis",
   JOURNAL   = "SIAM J. Math. Anal.",
   VOLUME    = "2",
   NUMBER    = "",
   YEAR      = "1983",
   PAGES     = "",
   REFERRED  = "[Rall91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Rall84a,
   AUTHOR    = "Rall, Louis B.",
   TITLE     = "Differentiation in {P}ascal-{SC}: {T}ype {GRADIENT}",
   JOURNAL   = "ACM Trans. Math. Software",
   VOLUME    = "10",
   NUMBER    = "2",
   PUBLISHER = "",
   MONTH     = "June",
   YEAR      = "1984",
   PAGES     = "161--184",
   REFERRED  = "[Arbe85a]; [Carl86a]; [Fisc87a]; [Gold91a]; 
                [Kalm91a]; [Neid87a]; 
                [Rall87a]; [Tesf91a].",
   COMMENT   = "Also appeared as {\sl MRC Technical Summary Report No. 2400,\/}
                Mathematics Research Center, University of Wisconsin-Madison
                (1982).",
   KEYWORDS  = "point algorithm; differentiation arithmetic.",
   ABSTRACT  = "The author shows how first order parital derivatives can be
               generated automatically using the language PASCAL--SC.  The
               form data structures used in the language are given, as well
               as the source code.  The resulting code is tested on the
               solution of nonlinear systems of equations using Newton's
               method.  The numerical example given is a simple 4 variable
               problem.",
}


@ARTICLE
{
   Rall86a,
   AUTHOR    = "Rall, Louis B.",
   TITLE     = "The arithmetic of differentiation",
   JOURNAL    = "Mathematics Magazine",
   VOLUME    = "59",
   PUBLISHER = "5",
   MONTH     = "December",
   YEAR      = "1986",
   PAGES     = "275--282",
   REFERRED  = "[Kalm91a]; [Mich91a]; [Neid87a]; [Neid89a]; 
                [Rall87a]; [Tesf91a].",
   COMMENT   = "Also appeared as {\sl MRC Technical Summary Report No. 2688,\/}
                Mathematics Research Center, University of Wisconsin-Madison.",
   KEYWORDS  = "differentiation arithmetic; groups; rings.",
   ABSTRACT  = "The author discusses differentiation of a scalar function.  He
                formulates this as arithmetic on a two-tuple containing the
                value of the function and the value of the derivative of the
                function.  The arithmetic formed is shown to have various
                group and ring properties.  A second formulation similar to
                that for complex arithmetic using $ z = x+iy $ is also
                discussed.  The initial system setup is shown to work on a
                very simple example run on a programmable hand calculator.",
}


@TECHREPORT
{
   Rall85a,
   AUTHOR    = "Rall, Louis B.",
   TITLE     = "Global optimisation using automatic differentiation and
                interval arithmetic",
   TYPE      = "Technical Summary Report",
   NUMBER    = "No. 2832",
   INSTITUTION = "Mathematics Research Center, 
                University of Wisconsin - Madison",
   YEAR      = "1985",
   PAGES     = "",
   REFERRED  = "[Pric87a].",
   COMMENT   = "",
   KEYWORDS  = "Global constrained optimisation; differentiation arithmetic;
                interval iteration; numerical examples.",
   ABSTRACT  = "Using differentiation arithmetic, algorithms are presented for
                finding one or all of the critical points of a twice
                differentiable function.  These methods use interval
                iterations in the given (rectangular) region.  Guaranteed
                bounds are also given for all of the quantities of interest.
                The n-dimensional Rosenbrock function is used as the test
                problem.",
}


@INCOLLECTION
{
   Rall87a,
   AUTHOR    = "Rall, Louis B.",
   TITLE     = "Optimal implementation of differentiation arithmetic",
   BOOKTITLE = "Computerarithmetic",
   PUBLISHER = "Teubner, B. G.",
   ADDRESS   = "Stuttgart",
   EDITOR    = "Kaucher, Edgar W.
                and Kulisch, Ulrich W.
                and Ullrich, Christian",
   YEAR      = "1987",
   PAGES     = "287--295",
   REFERRED  = "",
   COMMENT   = "In [Kauc87a].  Also appeared as {\sl MRC Technical Summary
                Report No. 2920,\/} Mathematics Research Center, University of
                Wisconsin-Madison (1986).",
   KEYWORDS  = "differentiation arithmetic.",
   ABSTRACT  = "The concepts of differentiation arithmetic are compared with
                real arithmetic, complex arithmetic and general computer
                arithmetic.  The implementation of differentiation
                arithmetic is looked at in an optimal way, in the context of
                roundoff errors, for both partial derivatives and Taylor
                coefficients.",
}


@INCOLLECTION
{
   Rall90a,
   AUTHOR    = "Rall, Louis B.",
   TITLE     = "Differentiation Arithmetics",
   BOOKTITLE = "Computer Arithmetic and Self-Validating Numerical Methods",
   YEAR      = "1990",
   EDITOR    = "Ullrich, Christian",
   PUBLISHER = "Academic Press",
   ADDRESS   = "New York",
   PAGES     = "73--90",
   REFERRED  = "[Rall91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Rall91a,
   AUTHOR    = "Rall, Louis B.",
   TITLE     = "Point and Interval Differentiation Arithmetics",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "17--24",
   REFERRED  = "[Flan91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Rall71a,
   AUTHOR    = "Rall, Louis B.
                and Wanner, G.",
   TITLE     = "Experience with {L}ie series",
   JOURNAL   = "Meth. und Verfahren der Math. Physik",
   VOLUME    = "5",
   YEAR      = "1971",
   PAGES     = "29--42",
   REFERRED  = "[Rall80a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; automatic differentiation; Lie series.",
   ABSTRACT  = "",
}


@BOOK
{
   Rats84a,
   AUTHOR    = "Ratschek, H.
                and Rokne, J.",
   TITLE     = "Computer Methods for the Range of Functions",
   PUBLISHER = "Halsted Press, Wiley",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1984",
   REFERRED  = "[Rall91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Reit65a,
   AUTHOR    = "Reiter, Alan",
   TITLE     = "Automatic generation of {T}aylor coefficients {(TAYLOR)}",
   TYPE      = "Prog. 3",
   INSTITUTION = "Mathematics Research Center, 
                University of Wisconsin - Madison",
   YEAR      = "1965",
   PAGES     = "",
   REFERRED  = "[Rall80a]; [Rall81a].",
   COMMENT   = "",
   KEYWORDS  = "automatic differentiation; Taylor coefficients.",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Reit65b,
   AUTHOR    = "Reiter, Alan",
   TITLE     = "Compiler of differential expressions {(CODEX)}",
   TYPE      = "Research Prog. 3",
   INSTITUTION = "Mathematics Research Center, 
                University of Wisconsin - Madison",
   YEAR      = "1965",
   PAGES     = "",
   REFERRED  = "[Rall80a].",
   COMMENT   = "",
   KEYWORDS  = "precompiler.",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Reit67a,
   AUTHOR    = "Reiter, Alan",
   TITLE     = "Automatic generation of {T}aylor coefficients {(TAYLOR)} for the
                {CDC} 1604",
   TYPE      = "Technical Summary Report",
   NUMBER    = "No. 830",
   INSTITUTION = "Mathematics Research Center, 
                University of Wisconsin - Madison",
   YEAR      = "1967",
   PAGES     = "",
   REFERRED  = "[Garl85a] \# 1317; [Hali83a]; [Rall80a]; [Rall81a].",
   COMMENT   = "",
   KEYWORDS  = "automatic differentiation; Taylor coefficients; computer
                program.",
   ABSTRACT  = "This is a CDC 1604 program which computes the series
                expansion of a function with respect to one variable.  The
                basic theoretical results used are given are well as a
                listing of the program.",
}


@BOOK
{
   Ritt50a,
   AUTHOR    = "Ritt, J. F.",
   TITLE     = "Differential Algebra",
   PUBLISHER = "American Mathematical Society",
   SERIES    = "",
   ADDRESS   = "Washington, D.C.",
   YEAR      = "1950",
   REFERRED  = "[Berz91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Rose78a,
   AUTHOR    = "Rose, D. J. 
                and Tarjan, R. E.",
   TITLE     = "Data Structures and Network Algorithms",
   JOURNAL   = "SIAM J. Appl. Math.",
   VOLUME    = "34",
   NUMBER    = "",
   YEAR      = "1978",
   PAGES     = "177--197",
   REFERRED  = "[Grie91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Rose63a,
   AUTHOR    = "Rosenblatt, F. ",
   TITLE     = "Principles of Neurodynamics",
   PUBLISHER = "Spartan",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1963",
   REFERRED  = "[Saar91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MISC
{
   Rost91b,
   AUTHOR    = "Nicole Rostaing",
   TITLE     = "",
   HOWPUBLISHED = "Poster presented at {SIAM} {W}orkshop on
                {A}utomatic {D}ifferentiation of {A}lgorithms, 
                {B}reckenridge, Colo.",
   MONTH     = "January",
   YEAR      = "1991",
   REFERRED  = "[Char91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MISC
{
   Rost91a,
   AUTHOR    = "Rostaing, Nicole
                and Gaetano, M.",
   TITLE     = "Response to electronic mail survey",
   HOWPUBLISHED = "Personal communication",
   MONTH     = "March",
   YEAR      = "1991",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}

@INCOLLECTION
{
   Rote90a,
   AUTHOR    = "Rote, G.",
   TITLE     = "Path problems in graphs",
   BOOKTITLE = "Computational Graph Theory",
   YEAR      = "1990",
   EDITOR    = "",
   PUBLISHER = "Springer Verlag",
   ADDRESS   = "Berlin",
   SERIES    = "Computing Supplementum 7",
   PAGES     = "155--189",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Rume86a,
   AUTHOR    = "Rumelhart, David E.
                and McClelland, James L.
                and {the PDP Research Group}",
   TITLE     = "Parallel Distributed Processing. Explorations in the
                Microstructure of Cognition",
   PUBLISHER = "MIT Press",
   SERIES    = "",
   ADDRESS   = "",
   YEAR      = "1986",
   REFERRED  = "[Saar91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Saar91a,
   AUTHOR    = "Saarinen, Sirpa
                and Bramley, Randall
                and Cybenko, George",
   TITLE     = "Neural Networks, Backpropagation, and Automatic 
                Differentiation",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "31--42",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Saar91b,
   AUTHOR    = "Saarinen, Sirpa
                and Bramley, R.
                and Cybenko, George",
   TITLE     = "The numerical solution of neural network training problems",
   JOURNAL    = "SIAM J. Sci. Stat. Comput.",
   VOLUME    = "",
   NUMBER    = "",
   YEAR      = "submitted",
   PAGES     = "",
   REFERRED  = "[Saar91a].",
   NOTE      = "Issued as CSRD Technical Report No. 1089.",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Sawy84a,
   AUTHOR    = "Sawyer, Jr., J. W.",
   TITLE     = "First partial differentiation by computer with an 
                application to categorical data analysis",
   JOURNAL   = "The American Statistician",
   VOLUME    = "38",
   NUMBER    = "",
   YEAR      = "1984",
   PAGES     = "300--308",
   REFERRED  = "[Irim91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Sela80a,
   AUTHOR    = "Sela, J. G.",
   TITLE     = "Spectral Modeling at the {N}ational {M}eteorological {C}enter",
   JOURNAL   = "Monthly Weather Review",
   VOLUME    = "108",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1980",
   PAGES     = "1279--1292",
   REFERRED  = "[Navo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@PHDTHESIS
{
   Shah76a,
   AUTHOR    = "Shah, Piyush C. ",
   TITLE     = "Estimation of Properties in Petroleum Reservoirs",
   SCHOOL    = "California Institute of Technology",
   ADDRESS   = "",
   MONTH     = "",
   YEAR      = "1976",
   REFERRED  = "[Shah91a].",
   NOTE      = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Shah91a,
   AUTHOR    = "Shah, Piyush",
   TITLE     = "Application of Adjoint Equations to Estimation of
                Parameters in Distributed Dynamic Systems",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "181--190",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Skee89a,
   AUTHOR    = "Skeel, R. D.",
   TITLE     = "Safety in Numbers: {T}he Boundless Errors of Numerical 
                Computation",
   INSTITUTION = "Department of Energy",
   YEAR      = "1989",
   TYPE      = "Report",
   NUMBER    = "ER/25026--30",
   ADDRESS   = "",
   REFERRED  = "[Layn91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Soul86a,
   AUTHOR    = "Souli\'{e}, Edgar J.",
   TITLE     = "L'am\'{e}lioration de l'orbite d'une \'{e}toile
                double visuelle",
   JOURNAL   = "Astronomy and Astrophysics",
   VOLUME    = "164",
   NUMBER    = "",
   YEAR      = "1986",
   PAGES     = "408--414",
   REFERRED  = "[Soul91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Soul88a,
   AUTHOR    = "Souli\'{e}, Edgar J.",
   TITLE     = "A few examples of least squares optimization
                in physical chemistry and astronomy",
   BOOKTITLE = "Trends in Mathematical Optimization",
   YEAR      = "1988",
   EDITOR    = "Hoffmann, K.-H. 
                and Hiriart-Urruty, J. B.  
                and Lemar\'{e}chal, C.
                and Zowe, J. ",
   PUBLISHER = "Birkhauser Verlag",
   ADDRESS   = "Basel",
   PAGES     = "327--340",
   REFERRED  = "[Soul91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Soul89a,
   AUTHOR    = "Souli\'{e}, Edgar J.
                and Lesieur, Pierre C.",
   TITLE     = "Quantitative analysis of the electron paramagnetic 
                resonance spectrum of a {Uranium(III)} compound",
   JOURNAL   = "J. Chem. Soc., Faraday Trans. 1",
   VOLUME    = "85",
   NUMBER    = "12",
   YEAR      = "1989",
   PAGES     = "4053--4062",
   REFERRED  = "[Soul91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Soul91a,
   AUTHOR    = "Souli\'{e}, Edgar J.",
   TITLE     = "User's Experience with {F}ortran Precompilers for
                Least Squares Optimization Problems",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "297--306",
   REFERRED  = "[Garc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@PHDTHESIS
{
   Spee80a,
   AUTHOR    = "Speelpenning, B.",
   TITLE     = "Compiling Fast Partial Derivatives of Functions Given
                by Algorithms",
   SCHOOL    = "Department of Computer Science,
                University of Illinois at Urbana-Champaign",
   MONTH     = "January",
   YEAR      = "1980",
   ADDRESS   = "Urbana-Champaign, Ill.",
   REFERRED  = "[Arbe85a]; [Corl91a]; [Gayd91a]; 
                [Irim91a]; [Jued91a]; [Kubo91a]; 
                [Hali83a]; [Hill82a]; 
                [Pfei87a]; [Rall91a]; [Tesf91a]; [Thac91a].",
   COMMENT   = "Char -- good stuff",
   KEYWORDS  = "point algorithm; precompiler; numerical results.",
   ABSTRACT  = "This is the author's doctoral thesis.  It starts by
               comparing previous work in the area of symbolic
               differentiation of algorithms.  Specifically it considers
               the work of Warner in 1975, Joss in 1976 and Kedem in 1977.
               The conclusions reached in this discussion are that the work
               by Joss is the best in terms of improvement.  The author
               proceeds to describe how Joss' work can be improved in terms
               of speed, accuracy and space.  A package, Jake, is described
               which is a compiler that takes a Fortran 66 input definition
               of a function.  This input is limited in that only one
               subroutine can be specified, and that certain Fortran 66
               statements are disallowed.  Jake is instructed on how to
               perform its task by directives within the subroutine.
               Timing results are provided on the performance of the code
               produced by Jake over those where finite differencing is
               used.",
}


@BOOK
{
   Stac74a,
   AUTHOR    = "Stacey, W. M.",
   TITLE     = "Variational Methods in Nuclear Reactor Physics",
   PUBLISHER = "Academic Press",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1974",
   REFERRED  = "[Worl91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Stei86a,
   AUTHOR    = "Steinberg, Stanly 
                and Roache, Patrick J.",
   TITLE     = "Using {M}acsyma to Write {FORTRAN} Subroutines",
   JOURNAL   = "J. Symbolic Computation",
   YEAR      = "1986",
   PAGES     = "213--216",
   MONTH     = "June",
   VOLUME    = "2",
   NUMBER    = "2",
   REFERRED  = "[Char91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Step87a,
   AUTHOR    = "Stephens, Bruce R.
                and Pryce, John D.",
   TITLE     = "Passing functions in {F}ortran for automatic differentiation",
   TYPE      = "Technical Report",
   NUMBER    = "{AM}--87--13",
   INSTITUTION = "School of Mathematics, University of Bristol",
   ADDRESS   = "Bristol, U.K.",
   YEAR      = "1987",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "precompiler.",
   ABSTRACT  = "This is a survey of possible methods for passing a function
               defined by a high level language procedure to an automatic
               differentiation package.  The automatic differentiation
               package described in [Davi87a] is specifically considered.",
}


@MANUAL
{
   Step90a,
   AUTHOR    = "Stephens, Bruce R.
                and Pryce, John D.",
   TITLE     = "The {DAPRE/UNIX} Preprocessor Users' Guide v1.2",
   ORGANIZATION = "Royal Military College of Science at Shrivenham",
   ADDRESS   = "Shrivenham, U.K.",
   YEAR      = "1990",
   REFERRED  = "[Corl91a]; [Soul91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Step91a,
   AUTHOR    = "Stephens, Bruce R.
                and Pryce, John D.",
   TITLE     = "{DAPRE}: {A} Differentiation Arithmetic System for 
                {FORTRAN}",
   INSTITUTION = "Royal Military College of Science",
   YEAR      = "1991",
   TYPE      = "Technical Report",
   NUMBER    = "ACM--91--3",
   ADDRESS   = "Shrivenham, U.K.",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Stet86a,
   AUTHOR    = "Stetter, Hans J",
   TITLE     = "Algorithms for the Inclusion of Solutions of Ordinary
                Initial Value Problems",
   BOOKTITLE = "Equadiff 6: {P}roceedings of the International Conference
                on Differential Equations and Their Applications
                (Brno, 1985)",
   YEAR      = "1986",
   EDITOR    = "Jaram\'{i}r Vosmansk\'{y}
                and Milo\u{o}s Zl\'{a}mal",
   PUBLISHER = "Springer Verlag",
   SERIES    = "Lecture Notes in Mathematics",
   VOLUME    = "1192",
   PAGES     = "85--94",
   ADDRESS   = "Berlin",
   REFERRED  = "[Corl91a].",
}


@INCOLLECTION
{
   Stet90a,
   AUTHOR    = "Stetter, Hans J.",
   TITLE     = "Validated solution of initial value problems for {ODEs}",
   BOOKTITLE = "Computer Arithmetic and Self-Validating Numerical Methods",
   YEAR      = "1990",
   EDITOR    = "Ullrich, Christian",
   PUBLISHER = "Academic Press",
   ADDRESS   = "New York",
   PAGES     = "171--187",
   REFERRED  = "[Layn91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Stou77a,
   AUTHOR    = "Stoutemyer, David R.",
   TITLE     = "Automatic Error Analysis Using Computer Algebraic 
                Manipulation",
   JOURNAL   = "ACM Trans. Math. Software",
   YEAR      = "1977",
   VOLUME    = "3",
   NUMBER    = "1",
   PAGES     = "26--43",
   MONTH     = "March",
   REFERRED  = "[Char91a].",
   COMMENT   = "Char -- Automatic error analysis in REDUCE.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Stro86a,
   AUTHOR    = "Stroustrup, Bjarne",
   TITLE     = "The {C++} Programming Language",
   PUBLISHER = "Addison-Wesley",
   YEAR      = "1986",
   ADDRESS   = "Reading, Mass.",
   REFERRED  = "[Corl91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MANUAL
{
   STSC89a,
   AUTHOR    = "STSC",
   TITLE     = "{APL*PLUS} System for the {PC} - {U}ser's Manual",
   ORGANIZATION = "STSC, Inc.",
   ADDRESS   = "Rockville, Md.",
   YEAR      = "1988",
   REFERRED  = "[Garc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Tala91a,
   AUTHOR    = "Talagrand, Oliver",
   TITLE     = "The Use of Adjoint Equations in Numerical Modelling of the
                Atmospheric Circulation",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "169--180",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Tala87a,
   AUTHOR    = "Talagrand, Olivier
                and Courtier, P.",
   TITLE     = "Variational Assimilation of Meteorological Observations 
                with the Adjoint Vorticity Equation -- {P}art {I}. {T}heory",
   JOURNAL   = "Q. J. R. Meteorol. Soc.",
   VOLUME    = "113",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1987",
   PAGES     = "1311--1328",
   REFERRED  = "[Navo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Tesf91a,
   AUTHOR    = "Tesfatsion, Leigh",
   TITLE     = "Automatic Evaluation of Higher-Order Partial Derivatives
                for Nonlocal Sensitivity Analysis",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "157--165",
   REFERRED  = "[Dixo91a]; [Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Thac66a,
   AUTHOR    = "H. C. {Thacher, Jr.}",
   TITLE     = "Solution of transcendental equations by series reversion",
   JOURNAL   = "Comm. ACM",
   VOLUME    = "9",
   NUMBER    = "1",
   YEAR      = "1966",
   PAGES     = "10--11",
   REFERRED  = "[Laws91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Thac90a,
   AUTHOR    = "William Carlisle Thacker",
   TITLE     = "Large least-squares problems and the need for 
                automating the generation of adjoint codes",
   BOOKTITLE = "Computational Solution of Nonlinear Systems of 
                Equations",
   YEAR      = "1990",
   EDITOR    = "",
   PUBLISHER = "American Mathematical Society",
   ADDRESS   = "",
   SERIES    = "Lectures in Applied Mathematics, No. 26",
   PAGES     = "645--677",
   REFERRED  = "[Thac91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Thac91a,
   AUTHOR    = "Thacker, William Carlisle",
   TITLE     = "Automatic Differentiation from an Oceanographer's
                Perspective",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "191--201",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Thac88a,
   AUTHOR    = "Thacker, William Carlisle 
                and Long, R. B.",
   TITLE     = "Fitting Dynamics to Data",
   JOURNAL   = "J. Geophys. Res.",
   VOLUME    = "93",
   NUMBER    = "C2",
   YEAR      = "1988",
   PAGES     = "1227--1240",
   REFERRED  = "[Horw91a]; [Irim91a]; [Tala91a]; [Thac91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Tham69a,
   AUTHOR    = "Thames, Joseph M.",
   TITLE     = "{SLANG}, A Problem-Solving Language for Continuous-Model 
                 Simulation and Optimization",
   BOOKTITLE = "Proceedings of the ACM 24th National Conf.",
   PUBLISHER = "ACM",
   ADDRESS   = "New York",
   YEAR      = "1969",
   PAGES     = "",
   REFERRED  = "[Jued91a]; [Tham91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Tham75a,
   AUTHOR    = "Thames, Joseph M.",
   TITLE     = "Computing in Calculus",
   JOURNAL   = "Research/Development",
   VOLUME    = "",
   NUMBER    = "",
   YEAR      = "1975",
   PAGES     = "24--30",
   REFERRED  = "[Jued91a]; [Tham91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Tham82a,
   AUTHOR    = "Thames, Joseph M.",
   TITLE     = "The Evolution of Synthetic Calculus: {A} Mathematical 
                Technology for Advanced Architecture",
   BOOKTITLE = "Proceedings of the International Workshop on High-Level 
                Language Computer Architecture, University of Maryland
                (College Park, Md.)",
   PUBLISHER = "",
   YEAR      = "1982",
   PAGES     = "",
   REFERRED  = "[Jued91a]; [Tham91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MANUAL
{
   Tham89a,
   AUTHOR    = "Thames, Joseph M.",
   TITLE     = "{FORTRAN} {CALCULUS}: {A} New Implementation 
                of Synthetic Calculus",
   ORGANIZATION = "Digital Calculus Corp.",
   ADDRESS   = "Torrance, Calif.",
   YEAR      = "1989",
   REFERRED  = "[Jued91a]; [Tham91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Tham91a,
   AUTHOR    = "Thames, Joseph M.",
   TITLE     = "Synthetic Calculus:  {A} Paradigm for Mathematical
                Program Synthesis",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "263--272",
   REFERRED  = "[Jued91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Thun84a,
   author    = "M. Thune",
   title     = "A software package for stability analysis of 
                difference methods",
   booktitle = "{PDE} Software:  {M}odules, Interfaces and Systems",
   publisher = "North-Holland",
   ADDRESS   = "New York",
   year      = "1984",
   editor    = "B. Engquist 
                and T. Smedsaas",
   pages     = "89",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Tomo72a,
   AUTHOR    = "Tomovic, R.
                and Vukobratovic, M.",
   TITLE     = "General Sensitivity Theory",
   PUBLISHER = "Elsevier North-Holland",
   SERIES    = "",
   ADDRESS   = "New York",
   YEAR      = "1972",
   REFERRED  = "[Worl91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Tsuc88a,
   AUTHOR    = "Tsuchiya, T.
                and Iri, Masao",
   TITLE     = "Analysis of rounding errors in large systems of 
                nonlinear equations",
   JOURNAL   = "Proceedings of the Institute of Statistical Mathematics",
   VOLUME    = "36",
   NUMBER    = "",
   YEAR      = "1988",
   PAGES     = "1--22",
   NOTE      = "(In Japanese).",
   REFERRED  = "[Irim91a].",
   COMMENT   = "English translation available as {\it RMI 89-02}, 
                Department of Mathematical Engineering and 
                Instrumentation Physics, Faculty of Engineering, 
                University of Tokyo, 1989",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MANUAL
{
   Turn85a,
   AUTHOR    = "Turner, J. R.",
   TITLE     = "Pocket {APL} - Reference Guide",
   ORGANIZATION = "STSC, Inc.",
   ADDRESS   = "Rockville, Md.",
   YEAR      = "1985",
   REFERRED  = "[Garc91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Udwa76a,
   AUTHOR    = "Udwadia, F. E.
                and Shah, Piyush C.",
   TITLE     = "Identification of Structures Through Records Obtained 
                During Strong Earthquake Ground Motion",
   JOURNAL   = "J. Engineering for Industry",
   VOLUME    = "",
   NUMBER    = "",
   MONTH     = "November",
   YEAR      = "1976",
   PAGES     = "1347--1362",
   REFERRED  = "[Shah91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Ukko81a,
   AUTHOR    = "Ukkonen, E.",
   TITLE     = "On the Calculation of the Effects of Rounding Errors",
   JOURNAL   = "ACM Trans. Math. Software",
   VOLUME    = "7",
   NUMBER    = "",
   YEAR      = "1981",
   PAGES     = "259--271",
   REFERRED  = "[Irim91a]; [Kubo91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MANUAL
{
   UNIC91a,
   AUTHOR    = "UNICOS",
   TITLE     = "{UNICOS} Performance Utilities Reference Manual, 
                {SR}--2040 6.0",
   ORGANIZATION = "Cray Research, Inc.",
   ADDRESS   = "",
   YEAR      = "1991",
   REFERRED  = "[Saar91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Urba85a,
   AUTHOR    = "Urban, B.",
   TITLE     = "Maximum Error Growth in Simple Meteorological Models",
   INSTITUTION = "Ecole Nationale de la M\'{e}t\'{e}orologie",
   MONTH     = "",
   YEAR      = "1985",
   TYPE      = "Internal report",
   NUMBER    = "",
   ADDRESS   = "Toulouse, France",
   REFERRED  = "[Tala91a].",
   NOTE      = "(In French).",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   vHeu87a,
   author    = "van den Heuvel, P.
                and van Hulzen, J. A.
                and Goldman, Victor V.",
   title     = "Automatic generation of {FORTRAN}-coded {Jacobians} 
                and {Hessians}",
   booktitle = "Proceedings of {EUROCAL} 87",
   SERIES    = "Lecture Notes in Computer Science",
   VOLUME    = "378",
   year      = "1987",
   editor    = "J. Davenport",
   pages     = "120--131",
   publisher = "Springer Verlag",
   ADDRESS   = "New York",
   note      = "",
   REFERRED  = "[Char91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   vHul81a,
   AUTHOR    = "van Hulzen, J. A.",
   TITLE     = "Breuer's grow factor algorithm in computer algebra",
   BOOKTITLE = "Proceedings of the 1981 ACM Symposium on Symbolic and
                Algebraic Computation",
   YEAR      = "1981",
   EDITOR    = "Wang, P. S.",
   PUBLISHER = "ACM",
   ADDRESS   = "New York",
   PAGES     = "100--104",
   REFERRED  = "[Char91a]; [Gold91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   vHul83a,
   AUTHOR    = "van Hulzen, J. A.",
   TITLE     = "Code optimization of ultivariate polynomial schemes: 
                {A} pragmatic approach",
   BOOKTITLE = "{Computer Algebra, Eurocal 83 (European Computer 
                Algebra Conference, London, England, March 1983)}",
   YEAR      = "1983",
   EDITOR    = "",
   PUBLISHER = "Springer Verlag",
   ADDRESS   = "Heidelberg",
   SERIES    = "Lecture Notes in Computer Science No. 162",
   PAGES     = "286--300",
   REFERRED  = "[Char91a]; [Gold91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   vHul91a,
   AUTHOR    = "van Hulzen, J. A.",
   TITLE     = "{SCOPE} 1, {A} Source-Code Optimization Package for 
                {REDUCE} -- User's Manual",
   TYPE      = "{T}echnical {R}eport",
   INSTITUTION = "Univ. of Twente",
   YEAR      = "in preparation",
   NUMBER    = "",
   ADDRESS   = "",
   REFERRED  = "[Gold91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   vHul89a,
   AUTHOR    = "van Hulzen, J. A.
                and Hulshof, B. J. A. 
                and Gates, B. L. 
                and van Heerwaarden, M. C.",
   TITLE     = "A code optimization package for {REDUCE}",
   BOOKTITLE = "Proceedings of the 1989 International 
                Symposium on Symbolic and Algebraic Computation",
   YEAR      = "1989",
   EDITOR    = "Gonnet, Gaston H.",
   PUBLISHER = "ACM Press",
   ADDRESS   = "New York",
   PAGES     = "163--170",
   REFERRED  = "[Char91a]; [Gold91a].",
   COMMENT   = "Char -- van Hulzen's work is available within the GENTRAN 
                package in REDUCE.  GENTRAN is available over the 
                internet from the Reduce Network Library,
                reduce-net@rand.org.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@MASTERSTHESIS
{
   vIwa92a,
   AUTHOR    = "van Iwaarden, Ronald John",
   TITLE     = "Automatic Differentiation as Applied to the Truncated
                {N}ewton's Method for Unconstrained Nonlinear Optimization",
   SCHOOL    = "University of Colorado at Denver",
   YEAR      = "1992",
   ADDRESS   = "Denver, Colo.",
   MONTH     = "",
   REFERRED  = "",
   KEYWORDS  = "",
   COMMENT   = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Veyr90a,
   AUTHOR    = "Veyre, P.",
   TITLE     = "Study of the forecast skill with the {K}alman 
                filter technique",
   BOOKTITLE = "Proceedings of the International Symposium on Assimilation
                of Observations in Meteorology and Oceanography, World
                Meteorological Organization, Geneva, Switzerland",
   PUBLISHER = "",
   YEAR      = "1990",
   PAGES     = "460",
   REFERRED  = "[Tala91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Voli85a,
   AUTHOR    = "Volin, Yu. M.
                and Ostrovskii, G. M.",
   TITLE     = "Automatic computation of derivatives with the use of the
                multilevel differentiating technique 
                --- {I}: {A}lgorithmic basis",
   JOURNAL   = "Computers and Mathematics with Applications",
   VOLUME    = "11",
   NUMBER    = "",
   PUBLISHER = "",
   YEAR      = "1985",
   PAGES     = "1099--1114",
   REFERRED  = "[Irim91a]; [Kubo91a]; [Tesf91a]; [Wexl87a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; differentiation arithmetic;
                forward method; back method.",
   ABSTRACT  = "Consider the vector-valued function
                $$ y = f(x), \quad f : R^m \rightarrow R. $$
                The authors consider calculating the partial derivatives
                $$ \frac{\partial y}{\partial x_i} =
                \frac{\partial f}{\partial x_i} $$ for each $ 1 \le i \le m $.
                The first method of calculation, called the {\sl forward
                method \/}, uses the variational form
                $$ \partial y = \frac{\partial f}{\partial x_i} \partial x_i $$.
                The second method of calculation, called the {\sl back
                method \/}, uses the adjoint variational form
                $$ \partial \overline{x}_i = \left(\frac{\partial f}
                {\partial x_i}\right)^T \partial \overline{y} $$
                where $\overline{.}$ means adjoint variable and sign T means
                transposition.  The forward method has been discussed
                elsewhere in the literature, see [Rall81a].  The authors
                discuss the relative merits of both methods.  They provide
                results which show that the forward method is the more space
                efficient and the back method is the more time efficient.
                The authors combine the two methods to produce a
                {\sl multilevel method \/} which is a compromise of the two
                methods.  This has the property that the memory requirements
                are better than the back method and the time requirements are
                better than the forward method.",
}


@PHDTHESIS
{
   Wang84a,
   AUTHOR    = "Wang, J.-L.",
   TITLE     = "The Computation and Sensitivity Analysis of
                Economic Equilibrium",
   SCHOOL    = "Department of Economics, USC",
   YEAR      = "1984",
   ADDRESS   = "Los Angeles, Calif.",
   MONTH     = "",
   NOTE      = "",
   REFERRED  = "[Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@article
{
   Wang86a,
   AUTHOR    = "Paul S. Wang",
   TITLE     = "{FINGER}:  {A} symbolic system for automatic generation 
                of numerical programs in finite element analysis",
   JOURNAL   = "J. Symbolic Computation",
   YEAR      = "1986",
   VOLUME    = "2",
   NUMBER    = "3",
   PAGES     = "305--316",
   MONTH     = "September",
   REFERRED  = "[Char91a].",
   COMMENT   = "Char -- Includes a discussion of code optimization 
                techniques.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Warn75a,
   AUTHOR    = "Warner, D. D.",
   TITLE     = "A partial derivative generator.",
   TYPE      = "Computing Science Technical Report",
   NUMBER    = "No. 28",
   INSTITUTION = "Bell Telephone Laboratories",
   ADDRESS   = "Murray Hill, N.J.",
   YEAR      = "1975",
   REFERRED  = "[Carl86a]; [Hali83a]; [Hill82a]; [Spee80a].",
   COMMENT   = "",
   KEYWORDS  = "differentiation arithmetic; precompiler.",
   ABSTRACT  = "A precompiler is described which takes a specification of a
                function as input and produces a Fortran subroutine which
                will evaluate the component functions and the correpsonding
                Jacobian.  Many of the Fortran elementary functions are
                provided, as well as a facility which allows the user to
                specify their own differentiation rules.",
}


@ARTICLE
{
   Weng64a,
   AUTHOR    = "Wengert, R. E.",
   TITLE     = "A simple automatic derivative evaluation program",
   JOURNAL   = "Comm. ACM",
   VOLUME    = "7",
   NUMBER    = "8",
   PUBLISHER = "",
   YEAR      = "1964",
   PAGES     = "463--464",
   REFERRED  = "[Bell65a]; [Carl86a]; [Corl88a]; [Garc91a]; [Irim91a]; 
                [Kala83b]; [Laws88a]; [Laws91a];
                [Neid87a]; [Neid89a]; [Ostr71a]; 
                [Pfei87a]; [Tesf91a]; [Voli85a]; [Wexl87a]; 
                [Wilk64a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; differentiation arithmetic; computer
               program.",
   ABSTRACT  = "A procedure for automatic evaluation of total and partial
               derivatives of arbitrary algebraic functions is presented.
               The numerical values of derivatives are computed without
               developing analytic expressions for the derivatives.  The
               function is decomposed into a sequence of elementary
               expressions  A library is provided for differentiating of
               elementary functions."
}


@PHDTHESIS
{
   Werb74a,
   AUTHOR    = "Werbos, Paul",
   TITLE     = "Beyond Regression: {N}ew Tools for Prediction and 
                Analysis in the Behavioral Sciences",
   SCHOOL    = "Committee on Appl. Math., Harvard Univ.",
   ADDRESS   = "Cambridge, Mass.",
   MONTH     = "November",
   YEAR      = "1974",
   REFERRED  = "[Saar91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Werb82a,
   author    = "P. Werbos",
   title     = "Applications of Advances in Nonlinear Sensitivity Analysis",
   booktitle = "Systems Modeling and Optimization",
   editors   = "R. Drenick 
                and F. Kozin",
   publisher = "Springer Verlag",
   address   = "New York",
   pages     = "762--777",
   year      = "1982",
}
  

@ARTICLE
{
   Werb90a,
   AUTHOR    = "Werbos, Paul",
   TITLE     = "Backpropagation Through Time: What It Does and How
		To Do It.",
   JOURNAL   = "Proceedings of the IEEE",
   VOLUME    = "78",
   NUMBER    = "10",
   YEAR      = "1990",
   PAGES     = "1550--1560",
   REFERRED  = "[Saar91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Werb91a,
   AUTHOR    = "Werbos, Paul",
   TITLE     = "Adaptive Networks as Models or Controllers: From
	        Neural Nets to the General Case",
   BOOKTITLE = "Proceedings of the Eighth International
                Conference on Mathematical and Computer Modeling",
   YEAR      = "1991",
   EDITOR    = "Avula",
   PUBLISHER = "Pergamon Press",
   ADDRESS   = "",
   PAGES     = "",
   REFERRED  = "[Saar91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Wert68a,
   AUTHOR    = "Wertz, H. J.",
   TITLE     = "{SUPER-CODEX}: {S}upervisor plus compiler of differentiable
                expressions",
   INSTITUTION = "Mathematics Research Center, 
                University of Wisconsin - Madison",
   YEAR      = "1972",
   PAGES     = "",
   REFERRED  = "[Hali83a]; [Rall80a].",
   COMMENT   = "Also Rept. No. TOR--0172(9320)--12, SUPER-CODEX: Analytic
                differentiation of Fortran statements, The Aerospace
                Corporation, El Segundo, Calif. (1972).",
   KEYWORDS  = "precompiler.",
   ABSTRACT  = "",
}


@BOOK
{
   Wert88a,
   AUTHOR    = "Wertz, J. R.",
   TITLE     = "Spacecraft Attitude Determination and Control",
   PUBLISHER = "D. Reidel Publishing Co.",
   SERIES    = "",
   ADDRESS   = "Boston",
   YEAR      = "1988",
   REFERRED  = "[Layn91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Wexl87a,
   AUTHOR    = "Wexler, Anthony S.",
   TITLE     = "Automatic evaluation of derivatives",
   JOURNAL   = "Applied Mathematics and Computation",
   VOLUME    = "24",
   NUMBER    = "",
   YEAR      = "1987",
   PAGES     = "19--46",
   REFERRED  = "[Neid89a]; [Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "differentiation arithmetic; computer program.",
   ABSTRACT  = "This is an implementation of Wengbert's automatic
                differentiation method, see [Weng64a], which uses dynamic
                memory allocation.",
}


@ARTICLE
{
   Weis82a,
   AUTHOR    = "Weisbin, C. R.
                and others",
   TITLE     = "Sensitivity and Uncertainty Analysis of Reactor 
                Performance Parameters",
   JOURNAL   = "Advances in Nuclear Science and Technology",
   VOLUME    = "14",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1982",
   PAGES     = "",
   REFERRED  = "[Worl91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Wexl88a,
   AUTHOR    = "Wexler, Anthony S.",
   TITLE     = "An Algorithm for Exact Evaluation of
                Multivariate Functions and Their Derivatives to Any Order",
   JOURNAL   = "Computational Statistics and Data Analysis",
   VOLUME    = "6",
   NUMBER    = "",
   YEAR      = "1988",
   PAGES     = "1--6",
   REFERRED  = "[Tesf91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Wilk64a,
   AUTHOR    = "Wilkins, R. D.",
   TITLE     = "Investigation of a new analytic model for numerical
                derivative evaluation",
   JOURNAL   = "Comm. ACM",
   VOLUME    = "7",
   NUMBER    = "8",
   PUBLISHER = "",
   YEAR      = "1964",
   PAGES     = "465--471",
   REFERRED  = "[Bell65a].",
   COMMENT   = "",
   KEYWORDS  = "point algorithm; differentiation arithmetic; numerical
               results.",
   ABSTRACT  = "The technique for evaluating derivatives described in
               [Weng64a] is discussed.  The technique is shown to be both
               easy to use and accurate by use of specific examples.",
}


@BOOK
{
   Wilk63a,
   AUTHOR    = "Wilkinson, James H.",
   TITLE     = "Rounding Errors in Algebraic Processes",
   PUBLISHER = "Prentice-Hall Inc.",
   SERIES    = "",
   ADDRESS   = "Englewood Cliffs, N.J.",
   YEAR      = "1963",
   REFERRED  = "[Kubo91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@TECHREPORT
{
   Wint79a,
   AUTHOR    = "Winters, K. H.
                and Cliffe, K. A.",
   TITLE     = "A finite element study of driven laminar flow in 
                a square cavity",
   INSTITUTION = "{AERE} Harwell, Theoretical Physics Division",
   ADDRESS   = "Harwell, U.K.",
   YEAR      = "1979",
   TYPE      = "Technical Report",
   NUMBER    = "AERE -- R 9444",
   MONTH     = "",
   NOTE      = "",
   REFERRED  = "[Bisc91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@phdthesis
{
   Wirtf80a,
   AUTHOR    = "Michael C. Wirth",
   TITLE     = "On the Automation of Computational Physics",
   SCHOOL    = "University of California, Davis",
   YEAR      = "1980",
   MONTH     = "October",
   NOTE      = "Also available as Lawrence Livermore National Laboratory,
                Report UCRL-52996, Livermore, Calif. (October 1980).",
   REFERRED  = "",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INPROCEEDINGS
{
   Wirt81a,
   AUTHOR    = "Michael C. Wirth",
   TITLE     = "Automatic Generation of Finite Difference Equations and 
                {F}ourier Stability Analysis",
   BOOKTITLE = "{Proceedings of the 1981 ACM Symposium on Symbolic and
                Algebraic Computation}",
   YEAR      = "1981",
   EDITOR    = "Paul S. Wang",
   PAGES     = "73--78",
   ORGANIZATION = "ACM",
   ADDRESS   = "New York",
   REFERRED  = "[Char91a].",
   COMMENT   = "Char -- Automatic generation of finite difference equation.",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Wolf88a,
   AUTHOR    = "Wolfram, Stephen",
   TITLE     = "Mathematica: {A} System for Doing Mathematics by Computer",
   PUBLISHER = "Addison-Wesley",
   SERIES    = "",
   ADDRESS   = "Reading, Mass.",
   YEAR      = "1988",
   REFERRED  = "[Gold91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Wolf82a,
   AUTHOR    = "Philip Wolfe",
   TITLE     = "Checking the Calculation of Gradients",
   JOURNAL   = "ACM Trans. Math. Software",
   VOLUME    = "6",
   NUMBER    = "4",
   MONTH     = "",
   YEAR      = "1982",
   PAGES     = "337--343",
   REFERRED  = "[Bisc92b].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Wolf90a,
   AUTHOR    = "Wolfram, Stephen",
   TITLE     = "Mathematica: {A} System for Doing Mathematics by Computer",
   EDITION   = "2nd",
   PUBLISHER = "Addison-Wesley",
   SERIES    = "",
   ADDRESS   = "Reading, Mass.",
   YEAR      = "1990",
   REFERRED  = "[Char91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Woll65a,
   AUTHOR    = "Wollnik, H.",
   TITLE     = "Second order approximation of the three-dimensional 
                trajectories of charged particles in deflecting 
                electrostatic and magnetic fields",
   JOURNAL   = "Nuclear Instruments and Methods",
   VOLUME    = "34",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1965",
   PAGES     = "213 +",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Woll67a,
   AUTHOR    = "Wollnik, H.",
   TITLE     = "Second order transfer matrices of real magnetic and 
                electrostatic sector fields",
   JOURNAL   = "Nuclear Instruments and Methods",
   VOLUME    = "52",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1965",
   PAGES     = "250 +",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Woll68a,
   AUTHOR    = "Wollnik, H.",
   TITLE     = "Image aberrations of second order of electrostatic 
                sector fields",
   JOURNAL   = "Nuclear Instruments and Methods",
   VOLUME    = "59",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1965",
   PAGES     = "277 +",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Woll87a,
   AUTHOR    = "Wollnik, H.",
   TITLE     = "Charged Particle Optics",
   PUBLISHER = "Academic Press",
   SERIES    = "",
   ADDRESS   = "Orlando, Fl.",
   YEAR      = "1987",
   REFERRED  = "[Berz91a].",
   COMMENTS  = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Woll65b,
   AUTHOR    = "Wollnik, H. 
                and Ewald, H.",
   TITLE     = "The influence of magnetic and electric fringing fields 
                on the trajectories of charged particles",
   JOURNAL   = "Nuclear Instruments and Methods",
   VOLUME    = "36",
   NUMBER    = "",
   MONTH     = "",
   YEAR      = "1965",
   PAGES     = "93 +",
   REFERRED  = "[Berz91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Worl86a,
   AUTHOR    = "Worley, Brian
                and Wright, R. Q. 
                and Pin, F. G. 
                and Harper, W. V.",
   TITLE     = "Application of an Automated Procedure for Adding a 
                Comprehensive Sensitivity Calculation Capability to the 
                {ORIGEN2} Point Depletion and Radioactivity Decay Code",
   JOURNAL   = "Nucl. Sci. Eng.",
   VOLUME    = "94",
   NUMBER    = "180",
   YEAR      = "1986",
   PAGES     = "",
   REFERRED  = "[Horw91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@INCOLLECTION
{
   Worl91a,
   AUTHOR    = "Worley, Brian",
   TITLE     = "Experience with the Forward and Reverse Mode of {GRESS} in
                Contaminant Transport Modeling and Other Applications",
   BOOKTITLE = "Automatic Differentiation of Algorithms:
                Theory, Implementation, and Application",
   YEAR      = "1991",
   EDITOR    = "Griewank, Andreas
                and Corliss, George F.",
   PUBLISHER = "SIAM",
   ADDRESS   = "Philadelphia, Penn.",
   PAGES     = "307--315",
   REFERRED  = "",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Yosh87a,
   AUTHOR    = "Yoshida, T.",
   TITLE     = "Derivation of a Computational Process for Partial 
                Derivatives of Functions Using Transformations of
                a Graph",
   JOURNAL   = "Transactions of Information Processing Society of Japan",
   VOLUME    = "11",
   NUMBER    = "",
   YEAR      = "19",
   PAGES     = "1112--1120",
   REFERRED  = "[Grie91a].",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@ARTICLE
{
   Yosh89a,
   AUTHOR    = "Yoshida, T.",
   TITLE     = "Automatic derivative derivation system",
   JOURNAL   = "Transactions of Information Processing Society of Japan",
   VOLUME    = "30",
   NUMBER    = "7",
   YEAR      = "1989",
   PAGES     = "799--806",
   REFERRED  = "[Jued91a]; [Soul91a].",
   NOTE      = "(In Japanese).",
   COMMENT   = "",
   KEYWORDS  = "",
   ABSTRACT  = "",
}


@BOOK
{
   Zack71a,
   AUTHOR    = "Zacks, S.",
   TITLE     = "The Theory of Statistical Inference",
   YEAR      = "1971",
   PUBLISHER = "John Wiley and Sons",
   SERIES    = "",
   ADDRESS   = "New York",
   REFERRED  = "[Garc91a].",
   KEYWORDS  = "",
   ABSTRACT  = "",
}