%  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;