%  File:  all_brec.bib                      Updated:  22-NOV-1991, 02-Mar-1994
%
% 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, PA, 1991.
%
%     This bibliography represents the common bibliography for all of the
% papers in this volume.  Each author prepared a bibliography for her or
% his own paper.  The separate bibliographies were merged into a single
% BibTex database, and references from several other sources were added.
% Especially valuable contributions were made by bibliographic data
% bases previously compiled by Bruce Char, by David Gay and by
% Davis, Corliss, and Krenz [Davi88a].
%     This bibliography includes most of the work known to the editors
% in the area of automatic differentiation.  Because it includes all of
% the works cited by any paper in this volume, it includes many citations
% which are not directly related to automatic differentiation.  For
% example, it includes basic references in optimization, symbolic algebra
% systems, and several applications areas.
%     The electronic form of this bibliography contains many other works
% relating to automatic differentiation.  The electronic version
% is available from netlib (netlib at research.bell-labs.com).  Corrections and
% additions are welcome and should be sent to
%        Dr. George F. Corliss,
%        Department of Mathematics, Statistics,
%            and Computer Science,
%        Marquette University,
%        Milwaukee, WI  53233 USA,
%        georgec at boris.mscs.mu.edu.
%
% Assumes commands to get Russian digraphs:
%   \newcommand{\Yu}{{Yu}}
%   \newcommand{\Ye}{{Ye}}
%   \newcommand{\Ju}{{Ju}}

@Book{Aber88a,
  author =       "Oliver Aberth",
  title =        "Precise Numerical Analysis",
  publisher =    "William Brown",
  address =      "Dubuque, IA",
  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 =       "M. Abramowitz and I. A. Stegun",
  title =        "Handbook of Mathematical Functions",
  publisher =    "Dover",
  series =       "",
  address =      "New York",
  year =         "1970",
  referred =     "[Layn91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Adam69a,
  author =       "D. S. Adamson and C. W. Winant",
  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 {Ada} Programming Language,
                 {ANSI/MIL--STD--1815A}",
  organization = "",
  address =      "Washington, DC",
  year =         "1983",
  referred =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{AFNO83a,
  author =       "AFNOR",
  title =        "Le Langage de Programmation {FORTRAN}",
  institution =  "{Association} {Fran\c{c}aise} de {Normalisation},
                 {Tour} {Europe}, {Cedex} 7, {F}-92080 {Paris} {La}
                 {D\'{e}fense} {Cedex}",
  year =         "1983",
  type =         "norme {I}{S}{O} 1539 (norme {N}{F} {Z} 65-110)",
  number =       "",
  address =      "",
  referred =     "[Soul91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Book{Ahoa86a,
  author =       "A. V. Aho and R. Sethi and J. D. Ullman",
  title =        "Compilers: {Principles}, Techniques, and Tools",
  publisher =    "Addison-Wesley",
  series =       "",
  address =      "Reading, MA",
  year =         "1986",
  referred =     "[Thac91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Aida89a,
  author =       "K. R. Aida-zade and {\Yu}ri G. Evtushenko",
  title =        "Bystroe avtomaticheskoe differentsirovanie na
                 {{\`{E}}{V}{M}} ({Fast} 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{Alfe83a,
  author =       "G. Alefeld and J. Herzberger",
  title =        "Introduction to Interval Computations",
  publisher =    "Academic Press",
  series =       "",
  address =      "New York",
  year =         "1983",
  referred =     "[Irim91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Book{Ande79a,
  author =       "L. Anderson and Nail~H. Ibragimov",
  title =        "Lie-Backlund Transformations in Applications",
  publisher =    "Society for Industrial and Applied Mathematics",
  series =       "SIAM Studies in Applied Mathematics",
  address =      "Philadelphia, PA",
  year =         "1979",
  referred =     "[Mich91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Arbe86a,
  author =       "P. Arbenz and W. Gander",
  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 =       "M. Arbib",
  title =        "Brains, Machines, and Mathematics",
  publisher =    "Springer Verlag",
  series =       "",
  address =      "Berlin",
  year =         "1987",
  referred =     "[Saar91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Ball69a,
  author =       "William E. Ball",
  title =        "{BSOLVE}: {Solution} to a set of nonlinear equations
                 by {Marquardt}'s method",
  booktitle =    "Material and Energy Balance Computations",
  year =         "1969",
  editor =       "Ernest J. Henley and Edward M. Rosen",
  publisher =    "John Wiley and Sons",
  address =      "New York",
  pages =        "560 -- 566",
  referred =     "[Soul91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Ball73a,
  author =       "William E. Ball",
  title =        "The {BSOLVE} subroutine",
  booktitle =    "Optimization Techniques with {FORTRAN}",
  year =         "1973",
  editor =       "James L. Kuester and Joe H. Mize",
  publisher =    "McGraw-Hill",
  address =      "New York",
  pages =        "240 -- 250",
  referred =     "[Soul91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Bard74a,
  author =       "Y. Bard",
  title =        "Nonlinear Parameter Estimation",
  publisher =    "Academic Press",
  series =       "",
  address =      "New York",
  year =         "1974",
  referred =     "[Garc91a].",
  keywords =     "",
  abstract =     "",
}

@Techreport{Bart89a,
  author =       "M. C. Bartholomew-Biggs and Lawrence C. W. Dixon and
                 Z. Maany and M. Mohseninia",
  title =        "Three Papers on Automatic Differentiation Presented
                 at the {IFAC} {Symposium} on ``Dynamic Modelling &
                 Control of National Economies'', July 1989, Edinburgh,
                 Scotland",
  type =         "Technical Report",
  number =       "No. 223",
  institution =  "The Numerical Optimisation Center, Hatfield
                 Polytechnic",
  address =      "Hatfield, UK",
  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 =       "David Barton",
  title =        "On Taylor 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 =       "David Barton and I. M. Willers and R. V. M. Zahar",
  title =        "The automatic solution of ordinary differential
                 equations by the method of Taylor 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 language 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 =       "David Barton and I. M. Willers and R. V. M. Zahar",
  title =        "Taylor Series Methods for Ordinary Differential
                 Equations -- {An} Evaluation",
  booktitle =    "Mathematical Software",
  year =         "1971",
  editor =       "John Rice",
  publisher =    "Academic Press",
  address =      "New York",
  pages =        "369--390",
  referred =     "[Fisc87e].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Baue74a,
  author =       "F. L. Bauer",
  title =        "Computational graphs and rounding errors",
  journal =      "SIAM Journal on Numerical Analysis",
  volume =       "11",
  number =       "",
  year =         "1974",
  pages =        "87 -- 96",
  referred =     "[Char91a]; [Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Baur83a,
  author =       "W. Baur and V. Strassen",
  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 =       "Richard A. Becker and John M. Chambers and Allan R.
                 Wilks",
  title =        "The New {S} Language",
  publisher =    "{Wadsworth and Brooks/Cole}",
  series =       "Computer Science Series",
  address =      "Pacific Grove, CA",
  year =         "1988",
  referred =     "[Corl91a].",
}

@Techreport{Beda59a,
  author =       "L. M. Beda and L. N. Korolev and N. V. Sukkikh and T.
                 S. Frolova",
  title =        "Programs for automatic differentiation for the
                 machine {BESM}",
  type =         "{Technical} {Report}",
  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 =       "R. E. Bellman and Robert E. Kalaba",
  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 =       "R. E. Bellman and Harriet H. Kagiwada and Robert E.
                 Kalaba",
  title =        "{Wengert}'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 =       "Martin Berz",
  title =        "The Differential Algebra {FORTRAN} Precompiler
                 {DAFOR}",
  institution =  "Los Alamos National Laboratory",
  address =      "Los Alamos, NM",
  type =         "Technical Report AT--3",
  number =       "TN--87--32",
  month =        "",
  year =         "1987",
  referred =     "[Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Berz87b,
  author =       "Martin Berz",
  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 =       "Martin Berz",
  title =        "{Differential} 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 =       "Martin Berz",
  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 =       "Martin Berz",
  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 =       "Martin Berz",
  title =        "Differential algebra -- {A} new tool",
  booktitle =    "Proceedings of the 1989 IEEE Particle Accelerator
                 Conference",
  year =         "March 20 -- 23, 1989",
  editor =       "Floyd Bennet and Joyce Kopta",
  publisher =    "IEEE",
  address =      "",
  pages =        "",
  referred =     "[Mich91a].",
  comment =      "IEEE Catalog Number 89CH2669-0",
  keywords =     "",
  abstract =     "",
}

@Incollection{Berz89c,
  author =       "Martin Berz",
  title =        "The Description of Particle Accelerators using High
                 Order Perturbation Theory on Maps",
  booktitle =    "Physics of Particle Accelerators",
  volume =       "1",
  year =         "1989",
  editor =       "M. Month",
  publisher =    "American Institute of Physics",
  address =      "",
  pages =        "961 +",
  referred =     "[Berz91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Berz90a,
  author =       "Martin Berz",
  title =        "Differential Algebra Precompiler Version 3 ---
                 {Reference} Manual",
  institution =  "National Superconducting Cyclotron Laboratory,
                 Michigan State University",
  type =         "Technical Report",
  number =       "MSUCL -- 755",
  address =      "East Lansing, MI 48824",
  year =         "1990",
  referred =     "[Berz91a]; [Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Berz90b,
  author =       "Martin Berz",
  title =        "{COSY} {INFINITY} Version 3 Reference Manual",
  institution =  "National Superconducting Cyclotron Lab., Michigan
                 State University",
  type =         "Technical Report",
  number =       "MSUCL -- 751",
  address =      "East Lansing, MI 48824",
  year =         "1990",
  referred =     "[Berz91a]; [Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Berz90c,
  author =       "Martin Berz",
  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 =       "Martin Berz",
  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 =       "Martin Berz",
  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 =       "Martin Berz",
  title =        "The {DA} precompiler {DAFOR}",
  institution =  "Lawrence Berkeley National Laboratory",
  month =        "",
  year =         "1990",
  type =         "{Technical} {Report}",
  number =       "",
  address =      "Berkeley, CA",
  referred =     "[Berz91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Berz91a,
  author =       "Martin Berz",
  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 =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "",
  referred =     "[Flan91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Berz91b,
  author =       "Martin Berz",
  title =        "{COSY} {INFINITY} Version 4 Reference Manual",
  institution =  "National Superconducting Cyclotron Lab., Michigan
                 State University",
  type =         "Technical Report",
  number =       "MSUCL -- 771",
  address =      "East Lansing, MI 48824",
  year =         "1991",
  referred =     "[Berz91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Berz91c,
  author =       "Martin Berz",
  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 =       "M. C. Biggs",
  title =        "Minimization algorithms making use of non-quadratic
                 properties of the objective function",
  journal =      "Journal of the Institute of Mathematics and Its
                 Applications",
  volume =       "8",
  number =       "",
  year =         "1971",
  pages =        "315 -- 327",
  referred =     "[Garc91a].",
  keywords =     "",
  abstract =     "",
}

@Article{Bigg73a,
  author =       "M. C. Biggs",
  title =        "A note on minimization algorithms which make use of
                 non-quadratic properties of the objective function",
  journal =      "Journal of the Institute of Mathematics and Its
                 Applications",
  volume =       "12",
  number =       "",
  year =         "1973",
  pages =        "337 -- 338",
  referred =     "[Garc91a].",
  keywords =     "",
  abstract =     "",
}

@Incollection{Bisc91a,
  author =       "Christian Bischof",
  title =        "Issues in Parallel Automatic Differentiation",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  year =         "1991",
  editor =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "",
  referred =     "[Corl91a]; [Layn91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Bisc91b,
  author =       "Christian Bischof and Andreas Griewank and David
                 Juedes",
  title =        "Exploiting parallelism in automatic differentiation",
  institution =  "Mathematics and Computer Sciences Division, Argonne
                 National Laboratory",
  year =         "1991",
  type =         "Preprint",
  number =       "MCS--P204--0191",
  address =      "9700 South Cass Ave., Argonne, IL 60439--4801",
  month =        "",
  note =         "To be published in the proceedings of the 1991 ACM
                 International Supercomputing Conference.",
  referred =     "[Bisc91a].",
}

@Techreport{Bisc91c,
  author =       "Christian Bischof and James Hu",
  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 =      "9700 South Cass Ave., Argonne, IL 60439--4801",
  month =        apr,
  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 {Fortran} Programs",
  institution =  "Mathematics and Computer Science Division, Argonne
                 National Laboratory",
  month =        "",
  year =         "1991",
  type =         "Preprint",
  number =       "MCS--P263--0991",
  address =      "9700 S. Cass Ave., Argonne, IL 60439--4801",
  note =         "Also appeared as Technical Report 91185, Center for
                 Research in Parallel Computation, Rice University,
                 Houston, TX 77251.",
  referred =     "[Bisc91g]; [Bisc91h].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Bisc91g,
  author =       "Christian Bischof and Paul Hovland",
  title =        "Using {ADIFOR} to Compute Dense and Sparse
                 {Jacobians}",
  institution =  "Mathematics and Computer Science Division, Argonne
                 National Laboratory",
  month =        oct,
  year =         "1991",
  type =         "Technical Memorandum",
  number =       "ANL/MCS--TM--158",
  address =      "9700 S. Cass Ave., Argonne, IL 60439--4801",
  referred =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Bisc91i,
  author =       "Christian Bischof and George Corliss and Andreas
                 Griewank",
  title =        "{ADIFOR} Exception Handling",
  institution =  "Mathematics and Computer Science Division, Argonne
                 National Laboratory",
  month =        "",
  year =         "1991",
  type =         "Technical Memorandum",
  number =       "ANL/MCS--TM--159",
  address =      "9700 S. Cass Ave., Argonne, IL 60439--4801",
  referred =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Bohl87a,
  author =       "G. Bohlender and Ch. Ullrich and J. Wolff von
                 Gudenberg and Louis B. Rall",
  title =        "{Pascal}-{SC}, A Computer Language for Scientific
                 Computation",
  publisher =    "Academic Press",
  series =       "",
  address =      "New York",
  year =         "1987",
  referred =     "[Kubo91a]; [Layn91a].",
  keywords =     "",
  abstract =     "",
}

@Article{Bord56a,
  author =       "J. L. Bordewijk",
  title =        "Inter-Reciprocity Applied to Electrical Networks",
  journal =      "Applied Science Research, The Netherland, Sect. ~B",
  volume =       "6",
  number =       "",
  year =         "1956",
  pages =        "1 -- 74, ",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Boyl90a,
  author =       "A. Boyle and B. F. Caviness",
  title =        "Future Directions for Research in Symbolic Computing",
  publisher =    "SIAM",
  series =       "",
  address =      "Philadelphia, PA",
  year =         "1990",
  referred =     "[Gold91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Book{Brac68a,
  author =       "J. Bracken and G. P. McCormick",
  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 =       "J. N. Bramhall",
  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 =       "Richard P. Brent",
  title =        "Algorithms for Minimization without Derivatives",
  publisher =    "Prentice-Hall",
  series =       "",
  address =      "Englewood Cliffs, NJ",
  year =         "1973",
  referred =     "[Garc91a].",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Bren77a,
  author =       "Richard P. Brent and H. T. Kung",
  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 =       "Richard P. Brent and H. T. Kung",
  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{Broo83a,
  author =       "B. R. Brooks and R. E. Bruccoleri and B. D. Olafson
                 and D. J. States and S. Swaminathan and M. Karplus",
  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 =       "A. Brook and D. Kendrick and A. Meerhaus",
  title =        "{GAMS}: {A} User's Guide",
  publisher =    "Scientific Press",
  series =       "",
  address =      "Redwood City, CA",
  year =         "1988",
  referred =     "[Gayd91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Brow64a,
  author =       "K. L. Brown and R. Belbeoch and P. Bounin",
  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 =       "Melvin A. Breuer",
  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 =       "George D. Byrne and Alan C. Hindmarsh",
  title =        "Stiff {ODE} Solvers: {A} Review of Current and Coming
                 Attractions",
  journal =      "Journal of 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}.
                 {Nonlinear} 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}.
                 {Extension} 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 =       "D. G. Cacuci and M. C. G. Hall",
  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 =       "D. Callahan and K. Cooper and R. T. Hood and Ken
                 Kennedy and Linda M. Torczon",
  title =        "{ParaScope}: a parallel programming environment",
  journal =      "International Journal of Supercomputer Applications",
  volume =       "2",
  number =       "4",
  month =        dec,
  year =         "1988",
  pages =        "",
  referred =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Care87a,
  author =       "D. C. Carey",
  title =        "The Optics of Charged Particle Beams",
  publisher =    "Harwood",
  series =       "",
  address =      "",
  year =         "1987",
  referred =     "[Berz91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Carl86a,
  author =       "Bradley R. Carlile",
  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 =       "R. D. Carter and L. F. {Kemp, Jr.} and A. C. Pierce
                 and D. L. Williams",
  title =        "Performance Matching with Constraints",
  journal =      "Society of Petroleum Engineers Journal",
  volume =       "",
  number =       "",
  month =        apr,
  year =         "1974",
  pages =        "187 -- 196",
  referred =     "[Shah91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Chan67a,
  author =       "Y. F. Chang",
  title =        "The Conduction-Diffusion Theory of Semiconductor
                 Junctions",
  journal =      "Journal of Applied Physics",
  volume =       "38",
  number =       "2",
  year =         "1967",
  pages =        "534 -- 544",
  referred =     "[Corl91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Chan74a,
  author =       "Y. F. Chang",
  title =        "Automatic solution of differential equations",
  booktitle =    "Constructive and Computational Methods for
                 Differential and Integral Equations",
  series =       "Lecture Notes in Mathematics",
  volume =       "430",
  editor =       "D. L. Colton and R. P. Gilbert",
  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 =       "Y. F. Chang",
  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 =       "Y. F. Chang",
  title =        "A Variable-Order (10 -- $ \infty $) {Taylor} Series
                 Method for Solving {ODE}'s with Integration Steps
                 Almost Equal to the Radii of Convergence",
  howpublished = "Poster presented at {SIAM} {Workshop} on {Automatic}
                 {Differentiation}, {Breckenridge}, {CO}",
  month =        jan,
  year =         "1991",
  referred =     "[Corl91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Chan82a,
  author =       "Y. F. Chang and George F. Corliss",
  title =        "Solving Ordinary Differential Equations Using
                 {Taylor} Series",
  journal =      "ACM Trans. Math. Software",
  volume =       "8",
  number =       "2",
  year =         "1982",
  pages =        "114 -- 144",
  referred =     "[Corl91a]; [Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Chan81a,
  author =       "Y. F. Chang and Mike Tabor and John Weiss and George
                 F. Corliss",
  title =        "On the Analytic Structure of the {Henon}-{Heiles}
                 System",
  journal =      "Physics Letters",
  volume =       "85A",
  number =       "4",
  year =         "1981",
  pages =        "211 -- 213",
  referred =     "[Corl91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Char91a,
  author =       "Bruce W. Char",
  title =        "Computer Algebra as a Toolbox for Program Generation
                 and Manipulation",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  year =         "1991",
  editor =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "",
  referred =     "[Garc91a]; [Gold91a]; [Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Char86a,
  author =       "Bruce W. Char and G. J. Fee and Keith O. Geddes and
                 Gaston H. Gonnet and Michael B. Monagan",
  title =        "A Tutorial Introduction to {MAPLE}",
  journal =      "Journal of Symbolic Computation",
  volume =       "2",
  number =       "2",
  year =         "1986",
  pages =        "179 -- 200",
  referred =     "[Char91a]; [Gold91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Char88a,
  author =       "Bruce W. Char and Keith O. Geddes and Gaston H.
                 Gonnet and Michael B. Monagan and Stephen M. Watt",
  title =        "{MAPLE} Reference Manual",
  publisher =    "Watcom Publications",
  address =      "Waterloo, Ontario Canada",
  year =         "1988",
  referred =     "[Corl91a]; [Gold91a].",
  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 Journal",
  volume =       "",
  number =       "",
  month =        feb,
  year =         "1975",
  pages =        "74 -- 86",
  referred =     "[Shah91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Chao90a,
  author =       "W. C. Chao and L. P. Chang",
  title =        "Status of the development of a variational data
                 assimilation system using the adjoint method at
                 {Goddard} {Laboratory} for {Atmospheres}",
  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 Journal",
  volume =       "",
  number =       "",
  month =        dec,
  year =         "1974",
  pages =        "593 -- 608",
  referred =     "[Shah91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Chri90a,
  author =       "Bruce D. Christianson",
  title =        "Automatic {Hessians} by reverse accumulation",
  type =         "Technical Report",
  number =       "NOC TR228",
  institution =  "The Numerical Optimisation Center, Hatfield
                 Polytechnic",
  address =      "Hatfield, UK",
  month =        apr,
  year =         "1990",
  referred =     "[Bisc91a]; [Dixo91a]; [Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Misc{Chri91a,
  author =       "Bruce Christianson",
  title =        "Automatic {Hessians} by Reverse Accumulation in
                 {Ada}",
  howpublished = "Poster presented at {SIAM} {Workshop} on {Automatic}
                 {Differentiation}, {Breckenridge}, {CO}. Submitted to
                 {\sl {IMA} {Journal} of {Numerical} {Analysis}\/}",
  month =        jan,
  year =         "1991",
  referred =     "[Corl91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Civa65a,
  author =       "P. P.  Civalleri",
  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 =       "Frank H. Clark",
  title =        "Optimization and Nonsmooth Analysis",
  publisher =    "John Wiley and Sons",
  series =       "",
  address =      "New York",
  year =         "1983",
  referred =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Cole84a,
  author =       "T. F. Coleman and B. S. Garbow and J. J. Mor\'{e}",
  title =        "Software for estimating sparse {Jacobian} matrices",
  journal =      "ACM Trans. Math. Software",
  year =         "1984",
  volume =       "10",
  number =       "",
  pages =        "329 -- 345",
  month =        "",
  note =         "",
  referred =     "[Bisc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Cole83a,
  author =       "T. F. Coleman and J. J. Mor\'{e}",
  title =        "Estimation of sparse {Jacobian} matrices and graph
                 coloring problems",
  journal =      "SIAM Journal 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 =       "Grant O. {Cook, Jr.}",
  title =        "{ALPAL}, a Tool for the Development of Large-scale
                 Simulation Codes",
  institution =  "Lawrence Livermore National Laboratory",
  type =         "Technical Report",
  address =      " Berkley, CA",
  month =        aug,
  year =         "1988",
  number =       "UCID-21482",
  referred =     "[Char91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Corl87b,
  author =       "George F. Corliss",
  title =        "Performance of self-validating quadrature",
  booktitle =    "Proceedings of the NATO Advanced Workshop on
                 Numerical Integration: Recent Developments, Software,
                 and Applications",
  editor =       "Pat Keast and Graeme Fairweather",
  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 =       "George F. Corliss",
  title =        "Applications of Differentiation Arithmetic",
  booktitle =    "Reliability in Computing",
  publisher =    "Academic Press",
  editor =       "Ramon E. Moore",
  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 =       "George F. Corliss",
  title =        "Overloading Point and Interval {Taylor} Operators",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  year =         "1991",
  editor =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "",
  referred =     "[Jued91a]; [Kalm91a]; [Layn91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Corl82a,
  author =       "George F. Corliss and Y. F. Chang",
  title =        "Solving Ordinary Differential Equations Using
                 {Taylor} 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 =       "George F. Corliss and Paul H. Davis and Gary S. Krenz",
  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, WI 53233",
  month =        sep,
  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 methods 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 =       "Robert M. Corless and George F. Corliss",
  title =        "Automatic Differentiation in Validated Defect Control
                 for Ordinary Differential Equations",
  howpublished = "Poster presented at {SIAM} {Workshop} on {Automatic}
                 {Differentiation}, {Breckenridge}, {CO}. Submitted to
                 {\sl {IMA} {Journal} of {Numerical} {Analysis}\/}",
  month =        jan,
  year =         "1991",
  referred =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Corl87a,
  author =       "George F. Corliss and Louis B. Rall",
  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 =       "George F. Corliss and Louis B. Rall",
  title =        "Automatic generation of {Taylor} series in
                 {Pascal}-{SC}: {Basic} operations and applications to
                 differential equations",
  booktitle =    "Trans. of the First Army Conference on Applied
                 Mathematics and Computing (Washington, DC, 1983)",
  publisher =    "ARO Rep. 84-1, U. S. Army Res. Office",
  address =      "Research Triangle Park, NC",
  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 =       "George F. Corliss and Louis B. Rall",
  title =        "Computing the Range of Derivatives",
  booktitle =    "{IMACS} Annals on Computing and Applied Mathematics",
  year =         "to appear",
  pages =        "",
  publisher =    "{IMACS}",
  address =      "",
  series =       "{IMACS} Annals on Computing and Applied Mathematics",
  note =         "",
  referred =     "[Corl91a]; [Jued91a]; [Rall91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Cour85a,
  author =       "P. Courtier",
  title =        "Experiments in Data Assimilation Using the Adjoint
                 Model Technique",
  booktitle =    "Proceedings of the Workshop on High-Resolution
                 Analysis ECMWF (UK)",
  publisher =    "",
  month =        jun,
  year =         "1985",
  pages =        "",
  referred =     "[Navo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Cour87b,
  author =       "P. Courtier",
  title =        "Application of Optimal Control to Numerical
                 Meteorological Forecasting",
  type =         "{Doctoral} 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 =       "P. Courtier and Olivier Talagrand",
  title =        "Variational Assimilation of Meteorological
                 Observations with the Adjoint Equation -- {Part} {II}.
                 {Numerical} Results",
  journal =      "Q. J. R. Meteorol. Soc.",
  volume =       "113",
  number =       "",
  month =        "",
  year =         "1987",
  pages =        "1329 -- 1347",
  referred =     "[Navo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Cour90a,
  author =       "P. Courtier and Olivier Talagrand",
  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 =       "P. Courtier and J. N. Thepaut and Olivier Talagrand",
  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 =       "F. D. Crary",
  title =        "The {AUGMENT} precompiler. {II}. Technical
                 documentation",
  type =         "MRC Technical Summary Report",
  number =       "No. 1470",
  institution =  "Mathematics Research Center, University of
                 Madison-Wisconsin",
  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 =       "F. D. Crary",
  title =        "The {AUGMENT} precompiler. I. User information",
  type =         "MRC Technical Summary Report",
  number =       "No. 1469",
  institution =  "Mathematics Research Center, University of
                 Madison-Wisconsin",
  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 =       "F. D. Crary",
  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 =       "S. Datta and J. Nugent and A. Tishler and J. L. Wang",
  title =        "Seasonality, Differential Access, and Interlinking of
                 Labour and Credit",
  journal =      "Journal of Development Studies",
  year =         "to appear",
  volume =       "",
  number =       "",
  pages =        "",
  referred =     "[Tesf91a]",
}

@Book{Davi81a,
  author =       "A. J. T. Davie and R. Morrison",
  title =        "Recursive Descent Compiling",
  publisher =    "Ellis-Horwood",
  series =       "",
  address =      "Chichester",
  year =         "1981",
  referred =     "[Garc91a].",
  keywords =     "",
  abstract =     "",
}

@Techreport{Davi88a,
  author =       "Paul H. Davis and George F. Corliss and Gary S.
                 Krenz",
  title =        "A Bibliography on Methods and Techniques in
                 Differentiation Arithmetic",
  type =         "Technical Report",
  number =       "{AM}--88--09",
  institution =  "Maths. Dept., Bristol University",
  address =      "Bristol, UK",
  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 =       "Paul H. Davis and John D. Pryce",
  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, UK",
  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.",
}

@Techreport{Davi88b,
  author =       "Paul H. Davis and Bruce Stephens and George F.
                 Corliss and Gary S. Krenz",
  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, UK",
  year =         "1988",
  month =        sep,
  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 =       "John Dennis and David Gay and R. E. Welsch",
  title =        "Algorithm 573. {NL2SOL} --- {An} 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 =       "John Dennis and R. Schnabel",
  title =        "Numerical Methods for Unconstrained Optimization and
                 Nonlinear Equations",
  publisher =    "Prentice-Hall",
  year =         "1983",
  volume =       "",
  series =       "",
  address =      "Englewood Cliffs, NJ",
  edition =      "",
  month =        "",
  referred =     "[Bisc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Phdthesis{Derb85a,
  author =       "J. C. Derber",
  title =        "The Variational 4-D Assimilation of Analyses Using
                 Filtered Models as Constraints",
  school =       "University of Wisconsin-Madison",
  address =      "Madison, WI",
  month =        "",
  year =         "1985",
  referred =     "[Navo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Dewa89a,
  author =       "M. C. Dewar",
  title =        "{IRENA} --- {An} 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 =     "",
}

@Inproceedings{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 =        apr,
  series =       "Lecture Notes in Computer Science, No. 429.",
  note =         "",
  referred =     "[Char91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{LeDi82a,
  author =       "F.-X. {Le Dimet}",
  title =        "A General Formalism of Variational Analysis",
  institution =  "IMMS",
  month =        "",
  year =         "1982",
  type =         "Report",
  number =       "No. 22",
  address =      "Norman, OK 73091",
  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 =       "Y. K. Sasaki",
  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: {Theoretical} aspects",
  journal =      "Tellus",
  volume =       "38A",
  number =       "",
  year =         "1986",
  pages =        "97 -- 110",
  referred =     "[Thac91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Dixo87a,
  author =       "Lawrence C. W. Dixon",
  title =        "Automatic Differentiation and Parallel Processing in
                 Optimisation",
  type =         "Technical Report",
  number =       "No. 180",
  institution =  "The Numerical Optimisation Center, Hatfield
                 Polytechnic",
  address =      "Hatfield, UK",
  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 =       "Lawrence C. W. Dixon",
  title =        "Use of Automatic Differentiation for Calculating
                 {Hessians} and {Newton} Steps",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  year =         "1991",
  editor =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "",
  referred =     "[Grie91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Dixo87b,
  author =       "Lawrence C. W. Dixon and M. Mohseninia",
  title =        "The Use of the Extended Operations Set of {ADA} with
                 Automatic Differentiation and the Truncated {Newton}
                 Method",
  type =         "Technical Report",
  number =       "No. 176",
  institution =  "The Numerical Optimisation Center, Hatfield
                 Polytechnic",
  address =      "Hatfield, UK",
  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 =       "Lawrence C. W. Dixon and Z. Maany",
  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, UK",
  month =        feb,
  year =         "1988",
  pages =        "",
  referred =     "[Dixo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Dixo89b,
  author =       "Lawrence C. W. Dixon and Z. Maany",
  title =        "The Performance of the Truncated Newton, Conjugate
                 Gradient Algorithm in {Fortran} and {Ada}",
  type =         "Technical Report",
  number =       "NOC TR210",
  institution =  "The Numerical Optimisation Center, Hatfield
                 Polytechnic",
  address =      "Hatfield, UK",
  month =        jun,
  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 =       "Lawrence C. W. Dixon and Z. Maany and M. Mohseninia",
  title =        "Finite Element Optimization in {ADA} Using Automatic
                 Differentiation",
  type =         "Technical Report",
  number =       "NOC TR205",
  institution =  "The Numerical Optimisation Center, Hatfield
                 Polytechnic",
  address =      "Hatfield, UK",
  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 =       "Lawrence C. W. Dixon and Z. Maany and M. Mohseninia",
  title =        "Automatic Differentiation of Large Sparse Systems",
  journal =      "Journal of 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,
                 UK, July, 1989.",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Dixo87d,
  author =       "Lawrence C. W. Dixon and M. Mohseninia",
  title =        "The Use of the Extended Operations Set of {Ada} with
                 Automatic Differentiation and the Truncated {Newton}
                 Method",
  type =         "Technical Report",
  number =       "NOC TR176",
  institution =  "The Numerical Optimisation Center, Hatfield
                 Polytechnic",
  address =      "Hatfield, UK",
  month =        apr,
  year =         "1987",
  referred =     "[Dixo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Dixo86a,
  author =       "Lawrence C. W. Dixon and Richard C. Price",
  title =        "The Truncated {Gauss}-{Newton} Method for Sparse
                 Least Squares Problems Using Automatic
                 Differentiation",
  type =         "Technical Report",
  number =       "No. 171",
  institution =  "The Numerical Optimisation Center, Hatfield
                 Polytechnic",
  address =      "Hatfield, UK",
  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 =       "Lawrence C. W. Dixon and P. Dolan and Richard C.
                 Price",
  title =        "Finite Element Optimisation: {The} Use of Structured
                 Automatic Differentiation",
  type =         "Technical Report",
  number =       "No. 175",
  institution =  "The Numerical Optimisation Center, Hatfield
                 Polytechnic",
  address =      "Hatfield, UK",
  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 =       "Lawrence C. W. Dixon and Richard C. Price",
  title =        "The Truncated {Newton} Method for Sparse
                 Unconstrained Optimisation Using Automatic
                 Differentiation",
  type =         "Technical Report",
  number =       "NOC TR170",
  institution =  "The Numerical Optimisation Center, Hatfield
                 Polytechnic",
  address =      "Hatfield, UK",
  month =        oct,
  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 =       "Lawrence C. W. Dixon and Richard C. Price",
  title =        "The Truncated {Newton} Method for Sparse
                 Unconstrained Optimisation Using Automatic
                 Differentiation",
  journal =      "J. Opt. Theory and Appl.",
  volume =       "60",
  number =       "2",
  month =        feb,
  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 =       "L. C. W. Dixon and Richard C. Price",
  title =        "Numerical experience with the truncated {Newton}
                 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 =       "S. E. Dreyfus",
  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 =       "Y. Doleh and P. S. Wang",
  title =        "{SUI}: {A} system independent user interface for an
                 integrated scientific computing environment",
  booktitle =    "Proceedings ISSAC '90",
  year =         "1990",
  editor =       "S. Watanabe and M. Nagata",
  publisher =    "ACM-Press",
  address =      "New York",
  pages =        "88 -- 95",
  referred =     "[Gold91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Doua90a,
  author =       "D. Douady and Olivier Talagrand",
  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 =       "I. S. Duff and M. Anoli and N. I. M. Gould and J. K.
                 Reid",
  title =        "The Practical Use of the {Hellerman}-{Ranck} P$^4$
                 Algorithm and the P$^5$ Algorithm of {Erisman} 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 =       "R. Duffin",
  title =        "On {Fourier}'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, NY 10598",
  year =         "1968",
  number =       "320 -- 2956",
  month =        sep,
  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} Journal of Scientific and Statistical
                 Computing",
  year =         "1980",
  volume =       "1",
  number =       "2",
  pages =        "249 -- 259",
  month =        jun,
  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, MA",
  year =         "1990",
  referred =     "[Kalm91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Enri87a,
  author =       "Wayne H. Enright and John D. Pryce",
  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 =       "P. R. Escobal",
  title =        "Methods of Orbit Determination",
  edition =      "Second",
  publisher =    "Robert E. Krieger Publishing",
  series =       "",
  address =      "",
  year =         "1976",
  referred =     "[Layn91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Book{Evtu85a,
  author =       "{\Yu}ri G. Evtushenko",
  title =        "Numerical Optimization Techniques",
  publisher =    "Optimization Software Inc.",
  series =       "",
  address =      "New York",
  year =         "1985",
  referred =     "[Evtu91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Evtu91a,
  author =       "{\Yu}ri G. Evtushenko",
  title =        "Automatic Differentiation Viewed from Optimal
                 Control",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  year =         "1991",
  editor =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Evtu89b,
  author =       "{\Yu}ri G. Evtushenko and Vladimir P. Mazourik",
  title =        "Optimization Software",
  publisher =    "Znanie",
  series =       "",
  address =      "Moscow",
  year =         "1989",
  referred =     "[Evtu91a].",
  note =         "(In Russian).",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Evtu89a,
  author =       "{\Yu}ri G. Evtushenko and V. G. Zhadan",
  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 =       "Richard J. Fateman",
  title =        "Optimal Code for Serial and Parallel Computation",
  journal =      "Comm. ACM",
  year =         "1969",
  volume =       "12",
  number =       "12",
  pages =        "694 -- 695",
  month =        dec,
  referred =     "[Char91a].",
  comment =      "Discusses Breuer's paper as it relates to symbolic
                 algebra.",
  keywords =     "",
  abstract =     "",
}

@Techreport{Feld90a,
  author =       "S. I. Feldman and David M. Gay and M. W. Maimone and
                 N. L. Schryer",
  title =        "A {Fortran}-to-{C} Converter",
  institution =  "AT\&T Bell Laboratories",
  address =      "Murray Hill, NJ 07974",
  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 {Fortran} 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 =       "D. E. Fields 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, TN 37830",
  referred =     "[Horw91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Phdthesis{Fisc90b,
  author =       "Hans-C. Fischer",
  title =        "Schnelle Automatische {Differentiation},
                 {Einsclie}{\ss}ungsmethoden und {Anwendungen}",
  school =       "Univ. Karlsruhe",
  address =      "",
  year =         "1990",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Misc{Fisc91a,
  author =       "Hans-C. Fischer",
  title =        "Differentiation Arithmetic and Applications in
                 {Pascal-XSC}",
  howpublished = "Poster presented at {SIAM} {Workshop} on {Automatic}
                 {Differentiation}, {Breckenridge}, {CO}",
  month =        jan,
  year =         "1991",
  referred =     "[Corl91a]; [Layn91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Fisc87a,
  author =       "Herbert Fischer",
  title =        "Automatic differentiation: {Fast} 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, Schwerpunktprogramm der
                 Deutschen Forschungsgemeinschaft Anwendunsbezogene
                 Optimierung und Steurung",
  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 =       "Herbert Fischer",
  title =        "Automatic differentiation: {Fast} method to compute
                 the quadratic form of {Hessian} 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 =       "Herbert Fischer",
  title =        "Automatic differentiation: {Fast} 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 =       "Herbert Fischer",
  title =        "Automatic differentiation: {Parallel} computation of
                 function, gradient and {Hessian} matrix",
  journal =      "Parallel Computing",
  volume =       "13",
  number =       "",
  year =         "1990",
  pages =        "101 -- 110",
  referred =     "[Bisc91a].",
  comment =      "",
  abstract =     "",
}

@Techreport{Fisc87d,
  author =       "Herbert Fischer",
  title =        "Berechnung des Gradienten mit Automatischen
                 Differenzieren",
  type =         "Technical Report",
  number =       "No. 103B",
  institution =  "Technische Universt{\"a}t M{\"u}nchen, Institut
                 f{\"u}r Angewandte Mathematik und Statistik",
  month =        dec,
  year =         "1987",
  referred =     "[Fisc87a]; [Fisc87e].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Fisc87e,
  author =       "Herbert Fischer",
  title =        "Automatic Differentiation: How to Compute the
                 {Hessian} 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 =       "Herbert Fischer",
  title =        "Special Problems in Automatic Differentiation",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  year =         "1991",
  editor =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "",
  referred =     "[Garc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Fisc91c,
  author =       "Herbert Fischer",
  title =        "Automatic differentiation of the vector that solves a
                 parametric linear system",
  journal =      "J. of 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. of Symbolic Computation",
  pages =        "211 -- 227",
  volume =       "1",
  number =       "2",
  month =        jun,
  year =         "1985",
  referred =     "[Char91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Flaj87a,
  author =       "P. Flajolet and J.-M. Steyaert",
  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 =       "P. Flajolet and P. Sipala and J.-M. Steyaert",
  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 =       "Harley Flanders",
  title =        "Scientific Pascal",
  publisher =    "Prentice-Hall",
  series =       "",
  address =      "Englewood Cliffs, NJ",
  year =         "1984",
  referred =     "[Flan91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Flan91a,
  author =       "Harley Flanders",
  title =        "Automatic Differentiation of Composite Functions",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  year =         "1991",
  editor =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "",
  referred =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Misc{Flan91b,
  author =       "Harley Flanders",
  title =        "Response to electronic mail survey",
  howpublished = "Personal communication",
  month =        mar,
  year =         "1991",
  referred =     "[Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Flet65a,
  author =       "R. Fletcher",
  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 =       "R. Fletcher and J. A. J. Hall",
  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 =       "Etienne Forest and Martin Berz",
  title =        "Canonical Integration and Analysis of Periodic Maps
                 using {Non}-{Standard} Analysis and {Lie} Methods",
  booktitle =    "",
  year =         "1989",
  editor =       "",
  publisher =    "Springer Verlag",
  address =      "Berlin",
  pages =        "47 -- 66",
  referred =     "[Berz91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Fore89a,
  author =       "Etienne Forest and Martin Berz and John Irwin",
  title =        "Normal form methods for complicated periodic systems:
                 {A} complete solution using differential algebra and
                 {Lie} operators",
  journal =      "Particle Accelerators",
  volume =       "24",
  number =       "",
  year =         "1989",
  pages =        "91 +",
  referred =     "[Mich91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Four90a,
  author =       "R. Fourer and David M. Gay and B. W. Kernighan",
  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 =        jun,
  year =         "1978",
  pages =        "104 -- 126",
  referred =     "[Gayd91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Fran78a,
  author =       "P. M. Frank",
  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 =        feb,
  year =         "1991",
  type =         "Research Report",
  number =       "CS--TR--303--91",
  address =      "Princeton, NJ 08544",
  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 =        sep,
  number =       "3",
  referred =     "[Char91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Garc79a,
  author =       "Oscar Garc\'{\i}a",
  title =        "Modelling stand development with stochastic
                 differential equations",
  booktitle =    "Mensuration for Management Planning of Exotic Forest
                 Plantations",
  year =         "1979",
  editor =       "D. A. Elliot",
  publisher =    "New Zealand Forest Service, FRI Symposium No. 20",
  address =      "",
  pages =        "315 -- 333",
  referred =     "[Garc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Garc83a,
  author =       "Oscar Garc\'{\i}a",
  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 =       "Oscar Garc\'{\i}a",
  title =        "New class of growth models for even-aged stands: {\it
                 {Pinus} radiata} in {Golden} {Downs} {Forest}",
  journal =      "New Zealand Journal of Forestry Science",
  volume =       "14",
  number =       "",
  year =         "1984",
  pages =        "65 -- 88",
  referred =     "[Garc91a].",
  keywords =     "",
  abstract =     "",
}

@Incollection{Garc88a,
  author =       "Oscar Garc\'{\i}a",
  title =        "Experience with an advanced growth modelling
                 methodology",
  booktitle =    "Forest Growth Modelling and Prediction",
  year =         "1988",
  editor =       "A. R. Ek and S. R. Shifley and T. E. Burk",
  publisher =    "USDA Forest Service, General Technical Report NC-120",
  address =      "",
  pages =        "668 -- 675",
  referred =     "[Garc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Garc88b,
  author =       "Oscar Garc\'{\i}a",
  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 =       "Oscar Garc\'{\i}a",
  title =        "Growth Modelling -- {New} Developments",
  booktitle =    "Japan and New Zealand Symposium on Forestry
                 Management Planning",
  year =         "1989",
  editor =       "H. Nagumo and Y. Konohira",
  publisher =    "Japan Association for Forestry Statistics",
  address =      "",
  pages =        "",
  referred =     "[Garc91a].",
  keywords =     "",
  abstract =     "",
}

@Incollection{Garc91a,
  author =       "Oscar Garc\'{\i}a",
  title =        "A System for the Differentiation of {Fortran} Code
                 and an Application to Parameter Estimation in Forest
                 Growth Models",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  year =         "1991",
  editor =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "",
  referred =     "[Jued91a]; [Soul91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Gate85a,
  author =       "B. L. Gates",
  title =        "{GENTRAN}: {An} automatic code generation facility
                 for {REDUCE}",
  journal =      "ACM SIGSAM Bulletin",
  volume =       "75",
  number =       "",
  year =         "1985",
  pages =        " 24 -- 85",
  referred =     "[Gold91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{