%  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}}

@String{j-SIAM-J-NUMER-ANAL     = "SIAM Journal on Numerical Analysis"}

@String{j-SIAM-J-SCI-STAT-COMP  = "SIAM Journal on Scientific and Statistical
                                  Computing"}

@String{j-TOMS                  = "ACM Transactions on Mathematical Software"}

@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.",
%%%     license         = "public domain",
  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",
  editor =       "Floyd Bennet and Joyce Kopta",
  booktitle =    "Proceedings of the 1989 IEEE Particle Accelerator
                 Conference",
  title =        "Differential algebra -- {A} new tool",
  publisher =    "IEEE",
  address =      "",
  pages =        "",
  day =          "20--23",
  month =        mar,
  year =         "1989",
  abstract =     "",
  comment =      "IEEE Catalog Number 89CH2669-0",
  keywords =     "",
  referred =     "[Mich91a].",
}

@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 =         "1991",
  note =         "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 =         "1991",
  note =         "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 =         "1991",
  note =         "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 =         "1991",
  note =         "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{Gate86a,
  author =       "B. L. Gates",
  title =        "A numerical code generation facility for {REDUCE}",
  booktitle =    "Proceedings of the 1986 Symposium on Symbolic and
                 Algebraic Computation",
  month =        jul,
  year =         "1986",
  editor =       "Bruce W. Char",
  publisher =    "ACM-Press",
  address =      "New York",
  pages =        "94 -- 99",
  referred =     "[Char91a]; [Gold91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Gate87a,
  author =       "B. L. Gates",
  title =        "{GENTRAN} User's Manual, {REDUCE} Version",
  publisher =    "The RAND Corporation",
  series =       "",
  address =      "Santa Monica, CA",
  year =         "1987",
  referred =     "[Gold91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Gayd83a,
  author =       "David M. Gay",
  title =        "{ALGORITHM} 611 --- {Subroutines} for Unconstrained
                 Minimization Using a Model/Trust-Region Approach",
  journal =      "ACM Trans. Math. Software",
  volume =       "9",
  number =       "",
  month =        "",
  year =         "1983",
  pages =        "503 -- 524",
  referred =     "[Gayd91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Gayd91a,
  author =       "David M. Gay",
  title =        "Automatic Differentiation of Nonlinear {AMPL} 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 =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Misc{Gayd91b,
  author =       "David M. Gay",
  title =        "Response to electronic mail survey",
  howpublished = "Personal communication",
  month =        mar,
  year =         "1991",
  referred =     "[Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Gibb60a,
  author =       "A. Gibbons",
  title =        "A program for the automatic integration of
                 differential equations using the method of {Taylor}
                 series",
  journal =      "Comp. J.",
  volume =       "3",
  year =         "1960",
  pages =        "108 -- 111",
  referred =     "[Bart70a]; [Chan74a]; [Corl82a]; [Hali83a].",
  comment =      "",
  keywords =     "point algorithm; computer program; Taylor series.",
  abstract =     "This is a description of a Taylor series method. The
                 recurrence relations for simple functions are derived.
                 Examples of how systems can be presented to an
                 implementation of the theory are given.",
}

@Article{Gilb91a,
  author =       "J. Ch. Gilbert",
  title =        "Automatic Differentiation and Iterative Processes",
  journal =      "Optimization Methods and Software",
  volume =       "",
  number =       "",
  year =         "1991",
  note =         "To appear.",
  pages =        "",
  referred =     "",
  note =         "Also appeared as Preprint, INRIA, Le Chesnay, France,
                 1991.",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Gold84a,
  author =       "D. Goldfarb and P. Toint",
  title =        "Optimal estimation of {Jacobian} and {Hessian}
                 matrices that arise in finite difference calculations",
  journal =      "Mathematics of Computation",
  year =         "1984",
  volume =       "",
  number =       "",
  pages =        "69 -- 88",
  month =        "",
  referred =     "[Bisc91a].",
  keywords =     "",
  abstract =     "",
}

@Incollection{Gold91a,
  author =       "Victor V. Goldman and J. Molenkamp and J. A. van
                 Hulzen",
  title =        "Efficient Numerical Program Generation and Computer
                 Algebra Environments",
  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 =     "[Char91a]; [Garc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Gome90a,
  author =       "C. Gomez",
  title =        "{MACROFORT}: {A} {FORTRAN} code generator for
                 {MAPLE}",
  institution =  "INRIA",
  year =         "1990",
  type =         "Rapports Techniques",
  number =       "119",
  address =      "",
  referred =     "[Gold91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Grah75a,
  author =       "Ron L. Graham",
  title =        "The Largest Small Hexagon",
  journal =      "J. Combinatorial Theory (A)",
  volume =       "18",
  number =       "",
  month =        "",
  year =         "1975",
  pages =        "165 -- 170",
  referred =     "[Gayd91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Gray67a,
  author =       "Julia H. Gray and Rall Louis B.",
  title =        "{NEWTON}: {A} general purpose program for solving
                 nonlinear equations",
  booktitle =    "Proc. 1967 Army Numerical Analysis Conference",
  publisher =    "U.S. Army Research Office",
  address =      "Research Triangle Park, NC",
  year =         "1967",
  pages =        "11 -- 59",
  referred =     "[Kuba72a]; [Rall80a]; [Rall84a].",
  comment =      "Also MRC Technical Summary Report No. 790,
                 Mathematics Research Center, University of
                 Madison-Wisconsin.",
  keywords =     "point algorithm; computer program; non-linear
                 equations; differentiation arithmetic.",
  abstract =     "A program is described which uses Newton's method for
                 solving a system of non-linear equations. The Jacobian
                 is calculated using differentiation arithmetic.
                 Automatic error analysis is provided by using
                 differentiation arithmetic to calculate the Hessian.",
}

@Techreport{Gray67b,
  author =       "Julia H. Gray and Allan Reiter",
  title =        "A compiler of differentiable expressions {(CODEX)}
                 for the {CDC} 3600",
  type =         "MRC Technical Summary Report",
  number =       "No. 791",
  institution =  "Mathematics Research Center, University of Wisconsin
                 - Madison",
  year =         "1967",
  pages =        "",
  referred =     "[Carl86a]; [Gray67a]; [Gray74a]; [Gray75a];
                 [Rall80a]; [Rall84a]; [Reit67b].",
  comment =      "",
  keywords =     "precompiler.",
  abstract =     "",
}

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

@Book{Gree76a,
  author =       "E. Greenspan",
  title =        "Developments in Perturbation Theory",
  publisher =    "Academic Press",
  series =       "Advances in Nuclear Science and Technology",
  volume =       "9",
  address =      "New York",
  year =         "1976",
  referred =     "[Worl91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Grie88a,
  author =       "Andreas Griewank",
  title =        "Book Review of {{\it Numerical Derivatives and
                 Nonlinear Analysis}}",
  journal =      "{SIAM Review}",
  year =         "1988",
  volume =       "30",
  number =       "2",
  pages =        "327 -- 329",
  month =        jun,
  comment =      "Book review -- note references given in this review.",
}

@Incollection{Grie89a,
  author =       "Andreas Griewank",
  title =        "On Automatic Differentiation",
  booktitle =    "Mathematical Programming: Recent Developments and
                 Applications",
  publisher =    "Kluwer Academic Publishers",
  year =         "1989",
  editor =       "M. Iri and K. Tanabe",
  pages =        "83 -- 108",
  address =      "",
  referred =     "[Bisc91a]; [Char91a]; [Corl91a]; [Dixo91a];
                 [Evtu91a]; [Garc91a]; [Gayd91a]; [Gold91a]; [Grie91a];
                 [Horw91a]; [Irim91a]; [Jued91a]; [Kubo91a]; [Mazo91a];
                 [Navo91a]; [Rall91a]; [Saar91a]; [Soul91a]; [Tesf91a];
                 [Thac91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Grie90c,
  author =       "Andreas Griewank",
  title =        "Direct Calculation of {Newton} Steps without
                 Accumulating {Jacobians}",
  booktitle =    "Large-Scale Numerical Optimization",
  year =         "1990",
  editor =       "T. F. Coleman and Yuying Li",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "115 -- 137",
  note =         "Also appeared as Preprint MCS--P132--0290,
                 Mathematics and Computer Science Division, Argonne
                 National Laboratory, 9700 S. Cass Ave., Argonne, IL
                 60439--4801.",
  referred =     "[Dixo91a]; [Grie91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Grie91b,
  author =       "Andreas Griewank",
  title =        "Achieving logarithmic growth of temporal and spatial
                 complexity in reverse automatic differentiation",
  institution =  "Mathematics and Computer Science Division, Argonne
                 National Laboratory",
  year =         "1991",
  type =         "Preprint",
  number =       "MCS--P228--0491",
  address =      "9700 S. Cass Ave., Argonne, IL 60439--4801",
  referred =     "[Bisc91a]; [Kubo91a].",
  comment =      "To appear in OMS",
  keywords =     "",
  abstract =     "",
}

@Incollection{Grie91c,
  author =       "Andreas Griewank",
  title =        "Automatic Evaluation of First- and Higher-Derivative
                 Vectors",
  booktitle =    "Proceedings of the Conference at W{\"u}rzburg, Aug.
                 1990, Bifurcation and Chaos: {Analysis}, Algorithms,
                 Applications",
  publisher =    "Birkh{\"a}user Verlag",
  year =         "1991",
  volume =       "97",
  editor =       "R. Seydel and F. W. Schneider and T. K{\"u}pper and
                 H. Troger",
  chapter =      "",
  pages =        "135 -- 148",
  address =      "Basel, Switzerland",
  month =        "",
  referred =     "[Bisc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Grie91d,
  author =       "Andreas Griewank",
  title =        "The Chain Rule Revisited in Scientific Computing",
  journal =      "SIAM News",
  volume =       "24",
  number =       "3 \& 4",
  month =        "May \& July",
  year =         "1991",
  pages =        "20 -- 21 \& 8 ff.",
  note =         "Also appeared as Preprint MCS--P227--0491,
                 Mathematics and Computer Science Division, Argonne
                 National Laboratory, 9700 S. Cass Ave., Argonne, IL
                 60439--4801.",
  referred =     "[Bisc91a]; [Kalm91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Grie91e,
  author =       "Andreas Griewank and George F. Corliss",
  title =        "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  year =         "1991",
  editor =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  referred =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Grie91f,
  author =       "Andreas Griewank",
  title =        "Sequential Evaluations of Adjoints and Higher
                 Derivative Vectors by Overloading and Reverse
                 Accumulation",
  institution =  "Konrad-Zuse-Zentrum f{\"u}r Informationstechnik
                 Berlin",
  year =         "1991",
  month =        jul,
  type =         "Preprint",
  number =       "SC 91--3",
  address =      "",
  referred =     "[Corl91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Grie90a,
  author =       "Andreas Griewank and David Juedes and Jay.
                 Srinivasan",
  title =        "{ADOL-C}, A Package for the Automatic Differentiation
                 of Algorithms Written in {C/C++}",
  institution =  "Mathematics and Computer Science Division, Argonne
                 National Laboratory",
  year =         "1990",
  type =         "Preprint",
  number =       "MCS--P180--1190",
  address =      "9700 S. Cass Ave., Argonne, IL 60439--4801",
  referred =     "[Bisc91a]; [Gayd91a]; [Gold91a]; [Grie91a];
                 [Jued91a]; [Kubo91a]; [Mich91a]; [Tesf91a].",
  comment =      "To appear in ACM Trans. Math. Software",
  keywords =     "",
  abstract =     "",
}

@Incollection{Grie91a,
  author =       "Andreas Griewank and Shawn Rees",
  title =        "On the Calculation of {Jacobian} matrices by the
                 {Markowitz} Rule",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  editor =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  year =         "1991",
  pages =        "",
  referred =     "[Corl91a]; [Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Hali83a,
  author =       "Hans J. Halin",
  title =        "The applicability of Taylor series methods in
                 simulation",
  booktitle =    "Proceedings of the 1983 Summer Computer Simulation
                 Conference (Vancouver, B.C)",
  volume =       "5",
  publisher =    "",
  year =         "1983",
  pages =        "",
  referred =     "",
  comment =      "",
  keywords =     "differentiation arithmetic; Taylor series; computer
                 program; numerical results; convergence.",
  abstract =     "The author surveys historical and current
                 developments in the application of recurrent Taylor
                 series to the integration of systems of ordinary
                 differential equations. The historical development of
                 the subject is reviewed along with a discussion of the
                 reasons for the existence of present day prejudice
                 against the method. A summary of current techniques is
                 presented including those for deriving the recurrence
                 relations with particular emphasize towards
                 implementation. Questions about convergence, stepsize
                 control and automatic control of series length are
                 considered. Various difficulties such as integration
                 across discontinuities and implicit differential
                 equations are discussed and accurate and efficient
                 remedies are provided. A simulation language, PSCSP
                 (Power Series Continuous-system Simulation Program),
                 is presented. This is used as a medium for testing and
                 comparing the theory discussed earlier.",
}

@Article{Hall82a,
  author =       "M. C. G. Hall and D. G. Cacuci and M. E. Schlesinger",
  title =        "Sensitivity analysis of a radiative-convective model
                 by the adjoint method",
  journal =      "J. Atmos. Sci.",
  volume =       "39",
  number =       "",
  month =        "",
  year =         "1982",
  pages =        "2038 -- 2050",
  referred =     "[Tala91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Hart67a,
  author =       "J. G. Hartwell",
  title =        "Simultaneous integration of N-bodies by analytic
                 continuation with recursively formed derivatives",
  journal =      "J. Astronomical Sci.",
  volume =       "XIV",
  number =       "4",
  year =         "1967",
  pages =        "173 -- 177",
  referred =     "[Chan74a].",
  comment =      "",
  keywords =     "point algorithms; differentiation arithmetic; Taylor
                 series; numerical results.",
  abstract =     "The paper describes how to set up the recursion
                 relations for the Taylor series method for the
                 N-bodies problem. Numerical results are provided which
                 compare the method for various tolerances and initial
                 conditions.",
}

@Incollection{Haye87a,
  author =       "K. J. Hayes and J. G. Hirschberg and D. J. Slottje",
  title =        "Computer Algebra: {Symbolic} and Algebraic
                 Computation in Economic/Econometric Applications",
  booktitle =    "Advances in Econometrics",
  volume =       "6",
  publisher =    "JAI Press, Inc.",
  year =         "1987",
  editor =       "",
  chapter =      "",
  pages =        "51 -- 89",
  address =      "",
  month =        "",
  referred =     "[Tesf91a]",
}

@Book{Hear87a,
  author =       "A. C. Hearn",
  title =        "{REDUCE} User's Manual, Version 3.3",
  publisher =    "The Rand Corporation",
  series =       "",
  address =      "Santa Monica, CA",
  year =         "1987",
  referred =     "[Gold91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Book{Hein71a,
  author =       "Wulff Dieter Heintz",
  title =        "Doppelsterne",
  publisher =    "Wilhelm Goldmann Verlag",
  series =       "",
  address =      "M{\"u}nchen",
  year =         "1971",
  pages =        "55 -- 73",
  referred =     "[Soul91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Henr56a,
  author =       "Peter Henrici",
  title =        "Automatic computations with power series",
  journal =      "J. ACM",
  volume =       "3",
  number =       "1",
  year =         "1956",
  pages =        "10 -- 15",
  referred =     "[Corl82a].",
  comment =      "",
  keywords =     "point algorithms; recursion relations.",
  abstract =     "The use of recursion relations in the calculation of
                 power series is suggested. The recursion relations for
                 two example power series are given.",
}

@Book{Henr64a,
  author =       "Peter Henrici",
  title =        "Elements of Numerical Analysis",
  publisher =    "John Wiley and Sons",
  series =       "",
  address =      "New York",
  year =         "1964",
  referred =     "[Kubo91a].",
  keywords =     "",
  abstract =     "",
}

@Book{Henr74a,
  author =       "Peter Henrici",
  title =        "Applied and Computational Complex Analysis, Vol. 1",
  publisher =    "John Wiley and Sons",
  series =       "",
  address =      "New York",
  year =         "1974",
  referred =     "[Flan91a]; [Rall91a].",
  keywords =     "",
  abstract =     "",
}

@Book{Hert91a,
  author =       "J. Hertz and A. Krough and R. Palmer",
  title =        "Introduction to the Theory of Neural Computation",
  publisher =    "Addison-Wesley",
  series =       "",
  address =      "Reading, MA",
  year =         "1991",
  referred =     "[Saar91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Heuv87a,
  author =       "P. van den Heuvel and J. A. van Hulzen and Victor V.
                 Goldman",
  title =        "Automatic generation of {FORTRAN}-coded {Jacobians}
                 and {Hessians}",
  booktitle =    "Proceedings of {EUROCAL} 87",
  series =       "Lecture Notes in Computer Science",
  volume =       "378",
  year =         "1987",
  editor =       "J. Davenport",
  pages =        "120 -- 131",
  publisher =    "Springer-Verlag",
  note =         "",
  referred =     "[Char91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Hill91a,
  author =       "David R. Hill and Lawrence C. Rich",
  title =        "Automatic Differentiation in {MATLAB}",
  journal =      "Applied Numerical Mathematics",
  volume =       "",
  number =       "",
  year =         "1991",
  note =         "To appear.",
  pages =        "",
  referred =     "[Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Hill82a,
  author =       "Kenneth E. Hillstrom",
  title =        "{JAKEF} - A portable symbolic differentiator of
                 functions given by algorithms",
  type =         "Technical Report",
  number =       "ANL--82--48",
  institution =  "Mathematics and Computer Science Division, Argonne
                 National Laboratory",
  address =      "9700 South Cass Ave., Argonne, IL 60439--4801",
  year =         "1982",
  referred =     "[Arbe85a].",
  comment =      "",
  keywords =     "symbolic differentiator; precompiler.",
  abstract =     "A precompiler, which is a {FORTRAN} version of that
                 writen by Speelpenning [Spee80a], is described.",
}

@Techreport{Hill85a,
  author =       "K. E. Hillstrom",
  title =        "Users Guide for {JAKEF}",
  institution =  "Mathematics and Computer Science Division, Argonne
                 National Laboratory",
  address =      "9700 South Cass Ave., Argonne, IL 60439--4801",
  year =         "1985",
  type =         "Technical Memorandum",
  number =       "ANL/MCS--TM--16",
  referred =     "[Corl91a]; [Garc91a]; [Gold91a]; [Irim91a];
                 [Jued91a]; [Kubo91a]; [Soul91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Book{Himm72a,
  author =       "D. M. Himmelblau",
  title =        "Applied Nonlinear Programming",
  publisher =    "McGraw-Hill",
  series =       "",
  address =      "New York",
  year =         "1972",
  referred =     "[Gayd91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Mastersthesis{Hort89a,
  author =       "S. Horton",
  title =        "Numerical Derivatives: {A} Comparative Study",
  school =       "Mathematics Department, University of Southern
                 California",
  year =         "1989",
  address =      "Los Angeles, CA 90089",
  month =        "",
  referred =     "[Tesf91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Horw89b,
  author =       "Jim E. Horwedel",
  title =        "Matrix Reduction Algorithms for {GRESS} and {ADGEN}",
  institution =  "Martin Marietta Energy Systems, Inc., Oak Ridge
                 National Laboratory",
  year =         "1989",
  type =         "Technical Memorandum",
  number =       "ORNL/TM 11261",
  address =      "Oak Ridge, TN 37830",
  referred =     "[Horw91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Horw91a,
  author =       "Jim E. Horwedel",
  title =        "{GRESS}: {A} Preprocessor for Sensitivity Studies on
                 {Fortran} Programs",
  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 =     "",
}

@Techreport{Horw88a,
  author =       "Jim E. Horwedel and Brian A. Worley and E. M. Oblow
                 and F. G. Pin",
  title =        "{GRESS} version 1.0 Users Manual",
  institution =  "Martin Marietta Energy Systems, Inc., Oak Ridge
                 National Laboratory",
  year =         "1988",
  type =         "Technical Memorandum",
  number =       "ORNL/TM 10835",
  address =      "Oak Ridge, TN 37830",
  referred =     "[Gold91a]; [Horw91a]; [Irim91a]; [Jued91a];
                 [Soul91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Horw89a,
  author =       "J. E. Horwedel and R. Q. Wright and R. E. Maerker",
  title =        "Sensitivity Analysis of {EQ3}",
  institution =  "Oak Ridge National Laboratory",
  year =         "1990",
  type =         "Technical Memorandum",
  number =       "ORNL/TM 11407",
  address =      "Oak Ridge, TN 37830",
  referred =     "[Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Horw90a,
  author =       "J. E. Horwedel and R. J. Raridon and R. Q. Wright",
  title =        "Sensitivity Analysis of {AIRDOS--EPA} Using {ADGEN}
                 with Matrix Reduction Algorithms",
  institution =  "Martin Marietta Energy Systems, Inc., Oak Ridge
                 National Laboratory",
  year =         "1989",
  type =         "Technical Memorandum",
  number =       "ORNL/TM 11373",
  address =      "Oak Ridge, TN 37830",
  referred =     "[Corl91a]; [Horw91a]; [Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{vHul81a,
  author =       "J. A. van Hulzen",
  title =        "Breuer's grow factor algorithm in computer algebra",
  booktitle =    "Proceedings of the 1981 ACM Symposium on Symbolic and
                 Algebraic Computation",
  year =         "1981",
  editor =       "P. S. Wang",
  publisher =    "ACM",
  address =      "New York",
  pages =        "100 -- 104",
  referred =     "[Char91a]; [Gold91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{vHul83a,
  author =       "J. A. van Hulzen",
  title =        "Code optimization of ultivariate polynomial schemes:
                 {A} pragmatic approach",
  booktitle =    "{Computer Algebra, Eurocal 83 (European Computer
                 Algebra Conference, London, UK, March 1983)}",
  year =         "1983",
  editor =       "",
  publisher =    "Springer-Verlag",
  address =      "Heidelberg",
  series =       "Lecture Notes in Computer Science No. 162",
  pages =        "286 -- 300",
  referred =     "[Char91a]; [Gold91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{vHul91a,
  author =       "J. A. van Hulzen",
  title =        "{SCOPE} 1, {A} Source-Code Optimization Package for
                 {REDUCE} -- User's Manual",
  type =         "{Technical} {Report}",
  institution =  "Univ. of Twente",
  year =         "1991",
  note =         "In preparation.",
  number =       "",
  address =      "",
  referred =     "[Gold91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{vHul89a,
  author =       "J. A. van Hulzen and B. J. A. Hulshof and B. L. Gates
                 and M. C. van Heerwaarden",
  title =        "A code optimization package for {REDUCE}",
  booktitle =    "Proceedings of the 1989 International Symposium on
                 Symbolic and Algebraic Computation",
  year =         "1989",
  editor =       "Gaston H. Gonnet",
  publisher =    "ACM-Press",
  address =      "New York",
  pages =        "163 -- 170",
  referred =     "[Char91a]; [Gold91a].",
  comment =      "Char -- van Hulzen's work is available within the
                 GENTRAN package in REDUCE. GENTRAN is available over
                 the internet from the Reduce Network Library,
                 reduce-net@rand.org.",
  keywords =     "",
  abstract =     "",
}

@Article{Huss90a,
  author =       "R. Huss",
  title =        "An {Ada} Library for Automatic Evaluation of
                 Derivatives",
  journal =      "Applied Mathematics and Computation",
  year =         "1990",
  volume =       "35",
  number =       "",
  pages =        "103 -- 123",
  month =        jan,
  note =         "Also appeared as Working Paper, Hughes Aircraft
                 Company, February, 1989.",
  referred =     "[Kalm91a]; [Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Manual{IBM90a,
  author =       "IBM",
  title =        "{IBM} High Accuracy Arithmetic - Extended Scientific
                 Computation",
  organization = "IBM",
  address =      "Mechanicsburg, PA",
  year =         "1990",
  note =         "IBM Publication No. SC33--6462--00.",
  referred =     "[Corl91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Irim62a,
  author =       "Masao Iri",
  title =        "Fundamentals of the algebraical and topological
                 treatments of general information networks",
  journal =      "RAAG Memoirs, G-V",
  volume =       "3",
  number =       "",
  year =         "1962",
  pages =        "418 -- 450",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Irim69a,
  author =       "Masao Iri",
  title =        "Network Flow, Transportation and Scheduling ---
                 Theory and Algorithms",
  publisher =    "Academic Press",
  series =       "",
  address =      "New York",
  year =         "1969",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Irim84a,
  author =       "Masao Iri",
  title =        "Simultaneous Computation of Functions, Partial
                 Derivatives and Estimates of Rounding Errors ---
                 {Complexity} and Practicality",
  journal =      "Japan Journal of Applied Mathematics",
  year =         "1984",
  volume =       "1",
  number =       "2",
  pages =        "223 -- 252",
  referred =     "[Corl91a]; [Evtu91a]; [Fisc91b]; [Horw91a];
                 [Irim91a]; [Kubo91a]; [Rall91a]; [Thac91a].",
  comment =      "",
  keywords =     "differentiation arithmetic; error estimates;
                 algebraic complexity.",
  abstract =     "This paper proves theoretical results about the
                 algebraic complexity involved in calculating the
                 partial derivatives of a function. It is shown that
                 the algebraic complexity of computing a function of
                 several variables and its partial derivatives with
                 respect to all of the variables is at most a constant
                 (four, five, six or seven which is independent of the
                 number of variables) times as large as that of
                 computing the function alone. Furthermore, it is seen
                 that a reasonable bound for the rounding error
                 incurred in the final function value is ready to
                 obtain once the function and its derivatives have been
                 computed according to the procedure described.",
}

@Incollection{Irim91a,
  author =       "Masao Iri",
  title =        "History of Automatic Differentiation and Error
                 Estimation",
  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]; [Kubo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Irim87a,
  author =       "Masao Iri and K. Kubota",
  title =        "Methods of Fast Automatic Differentiation and
                 Applications",
  institution =  "Department of Mathematical Engineering and
                 Information Physics, Faculty of Engineering,
                 University of Tokyo",
  year =         "1987",
  type =         "Research Memorandum",
  number =       "RMI 87 -- 02",
  address =      "",
  referred =     "[Evtu91a]; [Fisc91b]; [Gold91a]; [Irim91a];
                 [Kubo91a]; [Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Irim88a,
  author =       "Masao Iri and T. Tsuchiya and M. Hoshi",
  title =        "Automatic Computation of Partial Derivatives and
                 Rounding Error Estimates with Applications to
                 Large-scale Systems of Nonlinear Equations",
  journal =      "Journal of Computational and Applied Mathematics",
  volume =       "24",
  year =         "1988",
  pages =        "365 -- 392",
  referred =     "[Corl91a]; [Irim91a]; [Kubo91a].",
  comment =      "",
  note =         "Original Japanese version appeared in {\it Journal of
                 Information Processing}, 26 (1985), pp.~1411 -- 1420.",
  keywords =     "",
  abstract =     "",
}

@Book{Isaa66a,
  author =       "E. Isaacson and Herb B. Keller",
  title =        "Analysis of Numerical Methods",
  publisher =    "John Wiley and Sons",
  series =       "",
  address =      "New York",
  year =         "1966",
  referred =     "[Shah91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Mastersthesis{Iwat84a,
  author =       "N. Iwata",
  title =        "Automatization of the Computation of Partial
                 Derivatives",
  school =       "Graduate School, University of Tokyo",
  year =         "1984",
  address =      "",
  month =        "",
  referred =     "[Jued91a]; [Kubo91a].",
  note =         "(In Japanese).",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Iwat83a,
  author =       "N. Iwata and Masao Iri",
  title =        "Computation of the gradient of a function with many
                 variables",
  booktitle =    "Papers of the Special Interest Group on Numerical
                 Analysis",
  year =         "1983",
  editor =       "",
  publisher =    "Information Processing Society of Japan, 7-1",
  address =      "",
  pages =        "1 -- 10",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Jack86a,
  author =       "R. H. F. Jackson and G. P. McCormick",
  title =        "The polyadic structure of factorable function tensors
                 with applications to high-order minimization
                 techniques",
  journal =      "J. Opt. Theory Appl.",
  volume =       "51",
  number =       "",
  month =        "",
  year =         "1986",
  pages =        "63 -- 94",
  referred =     "[Fisc91b].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Jacq65a,
  author =       "P. Jacquard and C. Jain",
  title =        "Permeability Distributions from Field Pressure Data",
  journal =      "Society of Petroleum Engineers Journal",
  volume =       "",
  number =       "",
  month =        dec,
  year =         "1965",
  pages =        "281 -- 294",
  referred =     "[Shah91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Manual{JIS82a,
  author =       "{Japanese Industrial Standard}",
  title =        "Programming Language {FORTRAN}, {C6201 -- 1982}",
  organization = "",
  address =      "",
  year =         "1982",
  referred =     "[Kubo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Jerr89a,
  author =       "M. Jerrell",
  title =        "Automatic Differentiation and Function Minimization
                 in {C++}",
  booktitle =    "Proceedings of {OOP--SLA}",
  year =         "1989",
  editor =       "",
  publisher =    "ACM Press",
  chapter =      "",
  pages =        "18 -- 24",
  address =      "",
  month =        "",
  referred =     "[Jued91a]; [Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Jerr89b,
  author =       "M. Jerrell",
  title =        "Automatic Differentiation Using Almost Any Language",
  journal =      "ACM SIGNUM Newsletter",
  volume =       "",
  number =       "",
  year =         "1989",
  pages =        "2 -- 9",
  referred =     "[Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Jerr90a,
  author =       "M. Jerrell",
  title =        "Automatic Differentiation Using {C++}",
  journal =      "Journal of Object Oriented Programming",
  volume =       "",
  number =       "",
  year =         "1990",
  pages =        "17 -- 24",
  referred =     "[Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{John75a,
  author =       "S. C. Johnson",
  title =        "{YACC} --- {Yet} Another Compiler - Compiler",
  institution =  "Bell Laboratories",
  year =         "1975",
  type =         "Computing Science Technical Report",
  number =       "No. 32",
  address =      "Murray Hill, NJ 07974",
  referred =     "[Kubo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Jone91a,
  author =       "M. T. Jones and P. E. Plassmann",
  title =        "A Parallel Graph Coloring Heuristic",
  institution =  "Mathematics and Computer Science Division, Argonne
                 National Laboratory",
  month =        jun,
  year =         "1991",
  type =         "Preprint",
  number =       "MCS--P246-0691",
  address =      "9700 S. Cass Ave., Argonne, IL 60439--4801",
  referred =     "[Bisc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Phdthesis{Joss76a,
  author =       "Johan Joss",
  title =        "Algorithmishes Differenzieren",
  school =       "Eidgenoessische Technische Hochschule",
  address =      "Z{\"u}rich, Switzerland",
  year =         "1976",
  referred =     "[Spee80a].",
  comment =      "",
  keywords =     "point algorithm; precompiler; computer program;
                 numerical results.",
  abstract =     "",
}

@Incollection{Jued91a,
  author =       "David Juedes",
  title =        "A Taxonomy of Automatic Differentiation Tools",
  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 =     "[Bisc91a]; [Garc91a]; [Irim91a]; [Kubo91a];
                 [Mazo91a]; [Worl91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Jued90a,
  author =       "David Juedes and Andreas Griewank",
  title =        "Implementing Automatic Differentiation Efficiently",
  institution =  "Mathematics and Computer Sciences Division, Argonne
                 National Laboratory",
  year =         "1990",
  type =         "Technical Report",
  number =       "MCS--TM--140",
  address =      "9700 South Cass Ave., Argonne, IL 60439--4801",
  month =        "",
  referred =     "[Bisc91a]; [Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Kaba87a,
  author =       "K. Kabaya and Masoa Iri",
  title =        "Sum of uniformly distributed random variables and
                 family of nonanalytic ${C}^\infty$-functions",
  journal =      "Japan Journal of Applied Mathematics",
  volume =       "4",
  number =       "",
  year =         "1987",
  pages =        "1 -- 22",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Kaba88a,
  author =       "K. Kabaya-Imai and Masoa Iri",
  title =        "On operators defining a family of nonanalytic
                 ${C}^\infty$-functions",
  journal =      "Japan Journal of Applied Mathematics",
  volume =       "5",
  number =       "",
  year =         "1988",
  pages =        "333 -- 365",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

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

@Mastersthesis{Kahr53a,
  author =       "H. G. Kahrimanian",
  title =        "Analytical Differentiation by a Digital Computer",
  school =       "Temple University",
  year =         "1953",
  month =        may,
  referred =     "[Char91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Kala81a,
  author =       "R. Kalaba and Leigh Tesfatsion",
  title =        "Complete Comparative Static Differential Equations",
  journal =      "Nonlinear Analysis: Theory, Methods, and
                 Applications",
  year =         "1981",
  volume =       "5",
  number =       "",
  pages =        "821 -- 833",
  month =        "",
  referred =     "[Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Kala83a,
  author =       "Robert Kalaba and L. Tesfatsion and J. L. Wang",
  title =        "A finite table algorithm for the exact evaluation of
                 higher order partial derivatives of functions of many
                 variables",
  journal =      "J. Math. Anal. Appl.",
  volume =       "92",
  year =         "1983",
  pages =        "552 -- 563",
  referred =     "[Mich91a]; [Wexl87a].",
  comment =      "",
  keywords =     "point algorithm; differentiation arithmetic.",
  abstract =     "An algorithm is presented which is a systematic
                 extension of the algorithm presented in [Weng64a].
                 This allows the calculation of arbitrarily high orders
                 of partial derivatives of functions of many variables.
                 The method does not take advantage of sparsity in any
                 way, but the authors mention that it might be possible
                 to do so.",
}

@Article{Kala83b,
  author =       "Robert Kalaba and A. Tishler",
  title =        "A generalised Newton algorithm using higher-order
                 derivatives",
  journal =      "J. Opt. Theory and Appl.",
  volume =       "39",
  number =       "1",
  publisher =    "",
  year =         "1983",
  pages =        "1 -- 17",
  referred =     "",
  comment =      "",
  keywords =     "point algorithm; differentiation arithmetic; root
                 finding.",
  abstract =     "A Newton-type algorithm which uses first to rth order
                 partial derivatives is described. This reduces to the
                 Newton--Raphson algorithm if $ r = 2 $ . The partial
                 derivatives are calculated using the table method
                 described in [Kala83a]. A specific example is given to
                 show that the convergence of the method is faster than
                 that of the standard Newton--Raphson algorithm.",
}

@Article{Kala86a,
  author =       "R. Kalaba and Leigh Tesfatsion",
  title =        "Automatic Differentiation of Functions of
                 Derivatives",
  journal =      "Computers and Mathematics With Applications",
  year =         "1986",
  volume =       "12A",
  number =       "11",
  pages =        "1091 -- 1103",
  month =        nov,
  referred =     "[Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Kala90a,
  author =       "R. Kalaba and Leigh Tesfatsion",
  title =        "Nonlocal Automated Sensitivity Analysis",
  journal =      "Computers and Mathematics With Applications",
  year =         "1990",
  volume =       "20",
  number =       "",
  pages =        "53 -- 65",
  month =        "",
  referred =     "[Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Kala91a,
  author =       "R. Kalaba and Leigh Tesfatsion",
  title =        "Solving Nonlinear Equations by Adaptive Homotopy
                 Continuation",
  journal =      "Applied Mathematics and Computation",
  year =         "1991",
  volume =       "41",
  number =       "",
  pages =        "99 -- 115",
  month =        "",
  referred =     "[Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Kala81b,
  author =       "R. Kalaba and Leigh Tesfatsion and J. L. Wang",
  title =        "Local and Nonlocal Comparative Static Analysis of
                 Economic Systems",
  journal =      "Applied Mathematics and Computation",
  year =         "1981",
  volume =       "9",
  number =       "",
  pages =        "227 -- 234",
  month =        "",
  referred =     "[Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Kala83c,
  author =       "R. Kalaba and Leigh Tesfatsion and J.-L. Wang",
  title =        "A Finite Algorithm for the Exact Evaluation of
                 Higher-Order Partial Derivatives of Functions of Many
                 Variables",
  journal =      "Journal of Mathematical Analysis and Applications",
  volume =       "12",
  number =       "",
  year =         "1983",
  pages =        "181 -- 191",
  month =        "",
  referred =     "[Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Kala87a,
  author =       "R. Kalaba and T. Plum and Leigh Tesfatsion",
  title =        "Automation of Nested Matrix and Derivative
                 Operations",
  journal =      "Applied Mathematics and Computation",
  year =         "1987",
  volume =       "23",
  number =       "",
  pages =        "243 -- 268",
  month =        "",
  referred =     "[Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Kala84a,
  author =       "R. Kalaba and A. Tischler",
  title =        "Automatic Derivative Evaluation in the Optimization
                 of Nonlinear Models",
  journal =      "The Review of Economics and Statistics",
  year =         "1984",
  volume =       "66",
  number =       "",
  pages =        "653 -- 660",
  month =        "",
  referred =     "[Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Kalm91a,
  author =       "Dan Kalman and Robert Lindell",
  title =        "Automatic Differentiation in Astrodynamical Modeling",
  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 =     "",
}

@Article{Kalt88a,
  author =       "Erich Kaltofen",
  title =        "Greatest common divisors of polynomials given by
                 straight-line programs",
  journal =      "Journal of the Association for Computing Machinery",
  year =         "1988",
  volume =       "35",
  number =       "1",
  pages =        "231 -- 264",
  referred =     "[Char91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

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

@Techreport{Kalt90b,
  author =       "Erich Kaltofen and Michael F. Singer",
  title =        "Size Efficient Parallel Algebraic Circuits for
                 Partial Derivatives",
  institution =  "Department of Computer Science, Rensselaer
                 Polytechnic Institute",
  month =        oct,
  year =         "1990",
  type =         "Technical Report",
  number =       "No. 90-32",
  address =      "Troy, NY 12180--3590",
  referred =     "",
  comment =      "",
  note =         "To appear in World Scientific Publishing Co.
                 (Singapore) in the Proceedings of the IV International
                 Conference on Computer Algebra in Physical Research,
                 held at Dubna in the Soviet Union in May 1990.",
  keywords =     "",
  abstract =     "",
}

@Article{Kalt90a,
  author =       "Erich Kaltofen and Barry Trager",
  title =        "Computing with Polynomials Given by Black Boxes for
                 Their Evaluations: {Greatest} Common Divisors,
                 Factorization, Separation of Numerators and
                 Denominators",
  journal =      "Journal of Symbolic Computation",
  year =         "1990",
  volume =       "9",
  number =       "3",
  pages =        "301 -- 320",
  referred =     "[Char91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Kant57a,
  author =       "L. V. Kantorovich",
  title =        "Ob Odno{\u\i} Matematichesko{\u\i} Simvolike,
                 Udobno{\u\i} pri Provedenii Vychisleni{\u\i} na
                 Mashinakh",
  journal =      "Doklady Akademii Nauk SSSR",
  volume =       "113",
  number =       "4",
  year =         "1957",
  pages =        "738 -- 741",
  referred =     "[Irim91a]; [Kubo91a].",
  keywords =     "",
  abstract =     "",
}

@Book{Kauc84a,
  author =       "Edgar W. Kaucher and Willard L. Miranker",
  title =        "Self-Validating Numerics for Function Space Problems
                 --- {Computation} with Guarantees for Differential and
                 Integral Equations",
  publisher =    "Academic Press",
  series =       "",
  address =      "New York",
  year =         "1984",
  referred =     "[Irim91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

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

@Article{Kill85a,
  author =       "J. P. Killingsworth",
  title =        "Microcomputer Calculations in Physics",
  journal =      "Reports on Progress in Physics",
  year =         "1985",
  volume =       "48",
  number =       "",
  pages =        "54 -- 99",
  month =        "",
  referred =     "[Tesf91a].",
}

@Article{Kimk84a,
  author =       "K. V. Kim and Yu E. Nesterov and B. V.
                 Cherkasski{\u\i}",
  title =        "Otsenka Trudo\'{e}mkosti Vychisleniya Gradienta",
  journal =      "Doklady Akademii Nauk SSSR",
  volume =       "275",
  number =       "6",
  year =         "1984",
  pages =        "1306 -- 1309",
  referred =     "[Kubo91a].",
  keywords =     "",
  abstract =     "",
}

@Article{Kimk84b,
  author =       "K. V. Kim and Yu E. Nesterov and V. A. Skokov and B.
                 V. Cherkasski{\u\i}",
  title =        "\` Effektivny{\u\i} Algoritm Vychisleniya
                 Proizvodnykh i \` Ekstremal'nye Zadachi",
  journal =      "\` Ekonomika i Matematicheskie Metody",
  volume =       "20",
  number =       "2",
  year =         "1984",
  pages =        "309 -- 318",
  referred =     "[Irim91a]; [Kubo91a].",
  keywords =     "",
  abstract =     "",
}

@Article{Kimk85a,
  author =       "K. V. Kim and Yu E. Nesterov and V. A. Skokov and B.
                 V. Cherkasski{\u\i}",
  title =        "An Efficient Algorithm for Computing Derivatives and
                 Extremal Problems",
  journal =      "MATEKON",
  volume =       "21",
  number =       "",
  year =         "1985",
  pages =        "49 -- 67",
  referred =     "",
  keywords =     "",
  abstract =     "",
}

@Book{Klat90a,
  author =       "R. Klatte and U. Kulisch and M. Neaga and D. Ratz and
                 Ch. Ullrich",
  title =        "{PASCAL-XSC}: {A} {PASCAL} Extension for Scientific
                 Computation",
  publisher =    "Springer-Verlag",
  year =         "1990",
  note =         "To appear.",
  volume =       "",
  series =       "",
  address =      "Berlin",
  note =         "",
  referred =     "[Corl91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Knap68a,
  author =       "H. Knapp and G. Wanner",
  title =        "Numerical solution of ordinary differential equations
                 by {Groebner}'s method of {Lie}-series",
  type =         "Technical Summary Report",
  number =       "No. 880",
  institution =  "Mathematics Research Center, University of Wisconsin
                 - Madison",
  year =         "1968",
  referred =     "[Hali83a]; [Rall80a].",
  comment =      "",
  keywords =     "point algorithm; automatic differentiation; Lie
                 series.",
  abstract =     "",
}

@Techreport{Knap68b,
  author =       "H. Knapp and G. Wanner",
  title =        "{LIESE}: {A} program for ordinary differential
                 equations using {Lie}-series",
  type =         "Technical Summary Report",
  number =       "No. 881",
  institution =  "Mathematics Research Center, University of Wisconsin
                 - Madison",
  year =         "1968",
  pages =        "",
  referred =     "[Hali83a]; [Rall80a].",
  comment =      "",
  keywords =     "point algorithm; automatic differentiation; Lie
                 series.",
  abstract =     "",
}

@Techreport{Knap69a,
  author =       "H. Knapp and G. Wanner",
  title =        "{LIESE II}: {A} program for ordinary differential
                 equations using {Lie}-series",
  type =         "Technical Summary Report",
  number =       "No. 1008",
  institution =  "Mathematics Research Center, University of Wisconsin
                 - Madison",
  year =         "1969",
  pages =        "",
  referred =     "[Gray74a]; [Gray75a]; [Hali83a]; [Kuba72a];
                 [Rall80a].",
  comment =      "",
  keywords =     "point algorithm; automatic differentiation; Lie
                 series.",
  abstract =     "",
}

@Book{Knut81a,
  author =       "Donald E. Knuth",
  title =        "The Art of Computer Programming, Vol. 2.
                 Seminumerical Algorithms",
  publisher =    "Addison Wesley",
  series =       "",
  address =      "Reading, MA",
  year =         "1981",
  referred =     "[Laws91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Krin84a,
  author =       "B. Krinsky and Joseph Thames",
  title =        "The Structure of Synthetic Calculus",
  booktitle =    "Proceedings of the International Workshop on
                 High-Level Computer Architecture, University of
                 Maryland",
  publisher =    "",
  year =         "1984",
  pages =        "",
  referred =     "[Tham91a]; [Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Kuba72a,
  author =       "Dennis Kuba and Rall Louis B.",
  title =        "A {UNIVAC} 1108 program for obtaining rigorous error
                 estimates for approximate solutions of systems of
                 equations",
  type =         "Technical Summary Report",
  number =       "No. 1168",
  institution =  "Mathematics Research Center, University of Wisconsin
                 - Madison",
  year =         "1972",
  pages =        "",
  referred =     "[Gray75a]; [Rall84a].",
  comment =      "",
  keywords =     "interval algorithm; root finding; error estimates;
                 computer program; differentiation arithmetic.",
  abstract =     "A computer program is described which obtains, by use
                 of interval arithmetic, rigorous error bounds for
                 approximate solutions of finite systems of nonlinear
                 equations. The error bounds obtained include the
                 contributions of truncation error for Newton's method,
                 round-off error, and possible errors in the
                 coefficients of the given system of equations.",
}

@Incollection{Kubo88a,
  author =       "Koichi Kubota",
  title =        "A Preprocessor for Fast Automatic Differentiation ---
                 {Applications} and Difficulties on Practical Problems",
  booktitle =    "{RIMS} {Kokyuroku} 648 ``Fundamental Numerical
                 Algorithms and their Software''",
  year =         "1988",
  editor =       "",
  publisher =    "Research Institute for Mathematical Sciences, Kyoto
                 University",
  address =      "",
  pages =        "",
  referred =     "[Kubo91a].",
  note =         "(In Japanese).",
  comment =      "",
  abstract =     "",
}

@Phdthesis{Kubo89a,
  author =       "Koichi Kubota",
  title =        "Fast Automatic Differentiation and Applications",
  school =       "Division of Engineering of the Graduate School of the
                 University of Tokyo",
  address =      "",
  year =         "1989",
  referred =     "[Irim91a]; [Kubo91a].",
  note =         "(In Japanese).",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Kubo91a,
  author =       "Koichi Kubota",
  title =        "{PADRE2}, A {FORTRAN} Precompiler Yielding Error
                 Estimates and Second Derivatives",
  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 =     "",
}

@Article{Kubo88b,
  author =       "Koichi Kubota and Masao Iri",
  title =        "Formulation of Fast Automatic Differentiation and the
                 Analysis of its Complexity",
  journal =      "Transactions of Information Processing Society of
                 Japan",
  volume =       "29",
  number =       "",
  year =         "1988",
  pages =        "551 -- 560",
  referred =     "[Irim91a]; [Kubo91a].",
  note =         "(In Japanese).",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Kubo89b,
  author =       "Koichi Kubota and Masao Iri",
  title =        "Estimates of Rounding Errors with Fast Automatic
                 Differentiation and Interval Analysis",
  journal =      "Transactions of Information Processing Society of
                 Japan",
  volume =       "30",
  number =       "",
  year =         "1989",
  pages =        "807 -- 815",
  referred =     "[Irim91a]; [Kubo91a].",
  note =         "(In Japanese). Earlier English version is available
                 as {\it Research Memorandum} RMI 88--12, Department of
                 Mathematical Engineering and Instrumentation Physics,
                 Faculty of Engineering, University of Tokyo, 1988.",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Kubo90a,
  author =       "Koichi Kubota and Masao Iri",
  title =        "{PADRE2}, Version 1 --- {User}'s Manual",
  institution =  "Department of Mathematical Engineering and
                 Information Physics, Faculty of Engineering,
                 University of Tokyo",
  year =         "1990",
  type =         "Research Memorandum",
  number =       "RMI 90--01",
  address =      "",
  referred =     "[Jued91a]; [Kubo91a]; [Soul91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Kuli86a,
  author =       "Ulrich W. Kulisch and Willard L. Miranker",
  title =        "The arithmetic of the digital computer: {A} new
                 approach",
  journal =      "SIAM Review",
  volume =       "28",
  number =       "1",
  year =         "1986",
  pages =        "1 -- 40",
  referred =     "[Layn91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Laca88a,
  author =       "L. F. Lacarra and Olivier Talagrand",
  title =        "Short-range evolution of small perturbations in a
                 barotropic model",
  journal =      "Tellus",
  volume =       "40A",
  number =       "",
  month =        "",
  year =         "1988",
  pages =        "81 -- 95",
  referred =     "[Tala91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Lana81a,
  author =       "Douglas H. Lanam",
  title =        "An algebraic front-end for the production and use of
                 numeric programs",
  booktitle =    "Proceedings of the 1981 Symposium on Symbolic and
                 Algebraic Computation",
  year =         "1981",
  editor =       "P. S. Wang",
  pages =        "223 -- 227",
  organization = "Association of Computing Machinery",
  address =      "New York",
  month =        aug,
  referred =     "[Char91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Lars78a,
  author =       "J. L. Larson and A. H. Sameh",
  title =        "Efficient calculation of the effects of roundoff
                 errors",
  journal =      "{ACM Trans. Math. Software}",
  year =         "1978",
  volume =       "4",
  number =       "3",
  pages =        "228 -- 236",
  month =        sep,
  referred =     "[Char91a].",
  comment =      "Char -- First paper by Larson. Gives algorithm used
                 in [Lars80a].",
  keywords =     "",
  abstract =     "",
}

@Article{Lars80a,
  author =       "J. L. Larson and A. H. Sameh",
  title =        "Algorithms for Roundoff Error Analysis --- {A}
                 Relative Error Approach",
  journal =      "Computing",
  year =         "1980",
  volume =       "24",
  number =       "4",
  pages =        "275 -- 297",
  referred =     "",
  comment =      "Char -- Summary of Larson's thesis [Lars78a] which
                 describes complete error analyses which use Bauer's
                 computational graphs.",
  keywords =     "",
  abstract =     "",
}

@Techreport{Laws71a,
  author =       "Charles L. Lawson",
  title =        "Computing Derivatives Using {W}-Arithmetic and
                 {U}-Arithmetic",
  institution =  "Jet Propulsion Laboratory",
  address =      "Pasadena, CA 91105",
  month =        sep,
  year =         "1971",
  type =         "Internal Computing Memorandum",
  number =       "CM--286",
  referred =     "[Jued91a]; [Laws91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Laws88a,
  author =       "Charles L. Lawson",
  title =        "Series reversion as the reversed chain rule",
  journal =      "ACM SIGNUM Newsletter",
  volume =       "23",
  number =       "1",
  publisher =    "",
  month =        jan,
  year =         " 1988",
  pages =        "7 -- 9",
  referred =     "[Laws91a].",
  comment =      "",
  keywords =     "differentiation arithmetic; implicit functions.",
  abstract =     "Lawson gives Fortran subroutines for differentiation
                 arithmetic. A subroutine SWPRO for products
                 corresponds to Chang's ATS [Chang74a]. The chain rule
                 is implemented by repeated calls to SWPRO. Series
                 reversion for implicit functions is implemented by
                 reversing the chain rule. An application is given to
                 Keppler's equation, $M - E + e \sin (E) = 0$.",
}

@Incollection{Laws91a,
  author =       "Charles L. Lawson",
  title =        "Automatic Differentiation of Inverse 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 =     "[Flan91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Layn91a,
  author =       "J. Daniel Layne",
  title =        "Applying Automatic Differentiation and
                 Self-Validating Numerical Methods in Satellite
                 Simulations",
  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 =     "",
}

@Article{Lewi85a,
  author =       "J. M. Lewis and J. C. Derber",
  title =        "The Use of Adjoint Equations to Solve a Variational
                 Adjustment Problem with Advective Constraints",
  journal =      "Tellus",
  volume =       "37A",
  number =       "",
  month =        "",
  year =         "1985",
  pages =        "309 -- 322",
  referred =     "[Navo91a].",
  comment =      "Talagrand gives pages as 97 -- 110.",
  keywords =     "",
  abstract =     "",
}

@Techreport{Liep90a,
  author =       "M. Liepel and K. Schittkowski",
  title =        "{PCOMP}: {A} {FORTRAN} Code for Automatic
                 Differentiation",
  institution =  "DFG Schwerpunktprogramm Anwendungsbezogene
                 Optimierung und Optimale Steuerung, Mathematisches
                 Institut, Universit{\"a}t Bayreuth",
  year =         "1990",
  type =         "Report",
  number =       "No. 254",
  address =      "D-8580 Bayreuth, Germany",
  referred =     "[Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Lill70a,
  author =       "S. A. Lill",
  title =        "Algorithm 46: {A} modified {Davidon} method for
                 finding the minimum of a function using difference
                 approximation for derivatives",
  journal =      "The Computer Journal",
  volume =       "13, 14",
  number =       "",
  year =         "1970",
  pages =        "111 -- 113, 106",
  referred =     "[Garc91a].",
  keywords =     "",
  abstract =     "",
}

@Misc{Lind91a,
  author =       "R. Lindell",
  title =        "Response to electronic mail survey",
  howpublished = "Personal communication",
  month =        mar,
  year =         "1991",
  referred =     "[Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Linn76a,
  author =       "S. Linnainmaa",
  title =        "Taylor Expansion of the Accumulated Rounding Error",
  journal =      "BIT (Nordisk Tidskrift for Informationsbehandling)",
  volume =       "16",
  number =       "1",
  year =         "1976",
  pages =        "146 -- 160",
  referred =     "[Bisc91f]; [Char91a]; [Irim91a]; [Kubo91a].",
  keywords =     "",
  abstract =     "",
}

@Book{Lion71a,
  author =       "J. L. Lions",
  title =        "Optimal Control of Systems Governed by Partial
                 Differential Equations",
  publisher =    "Springer-Verlag",
  series =       "",
  address =      "Berlin",
  year =         "1971",
  referred =     "[Tala91a].",
  note =         "(Translation from the French edition, Dunod, Paris,
                 1969).",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

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

@Techreport{Liud88a,
  author =       "D. C. Liu and J. Nocedal",
  title =        "On the Limited Memory {BFGS} Method for Large Scale
                 Optimization",
  institution =  "Northwestern University",
  month =        "",
  year =         "1988",
  type =         "Technical Report",
  number =       "NAM 03",
  address =      "Evanston, IL",
  referred =     "[Navo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Lohn87a,
  author =       "Rudolph J. Lohner",
  title =        "Enclosing the solutions of ordinary initial and
                 boundary value problems",
  booktitle =    "Computer Arithmetic: {Scientific} Computation and
                 Programming Languages",
  year =         "1987",
  editor =       "Edgar W. Kaucher and Ulrich W. Kulisch and Christian
                 Ullrich",
  publisher =    "Wiley-Teubner Series in Computer Science",
  address =      "Stuttgart",
  pages =        "255 -- 286",
  referred =     "[Layn91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Lore81a,
  author =       "A. C. Lorenc",
  title =        "A global three-dimensional multivariate statistical
                 interpolation scheme",
  journal =      "Monthly Weather Review",
  volume =       "109",
  number =       "",
  month =        "",
  year =         "1981",
  pages =        "701 -- 721",
  referred =     "[Tala91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Lore88a,
  author =       "A. C. Lorenc",
  title =        "Optimal nonlinear objective analysis",
  journal =      "Q. J. R. Meteorol. Soc.",
  volume =       "114",
  number =       "",
  month =        "",
  year =         "1988",
  pages =        "205 -- 240",
  referred =     "[Tala91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Maan89a,
  author =       "Z. Maany",
  title =        "{Ada} Automatic Differentiation Package for the
                 Optimization of Functions of Many Variables",
  type =         "Technical Report",
  number =       "NOC TR209",
  institution =  "The Numerical Optimisation Center, Hatfield
                 Polytechnic",
  address =      "Hatfield, UK",
  month =        jul,
  year =         "1989",
  pages =        "",
  referred =     "[Dixo89b].",
  comment =      "",
  keywords =     "optimization",
  abstract =     "",
}

@Article{Maan89b,
  author =       "Z. A. Maany",
  title =        "{FORTRAN} Automatic Differentiation Package for the
                 Optimization of Functions of Many Variables",
  journal =      "",
  volume =       "",
  number =       "",
  month =        "",
  year =         "1989",
  note =         "To appear.",
  pages =        "",
  referred =     "[Dixo89b].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Marc74a,
  author =       "G. I. Marchuk",
  title =        "Numerical Solution of the Problems of the Dynamics of
                 the Atmosphere and Ocean",
  publisher =    "Gidrometeoizdat",
  series =       "",
  address =      "Leningrad",
  year =         "1974",
  referred =     "[Navo91a]; [Tala91a].",
  note =         "(In Russian).",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Maso53a,
  author =       "S. J. Mason",
  title =        "Feedback theory --- {Some} properties of signal flow
                 graphs",
  journal =      "Proceedings of IRE",
  volume =       "41",
  number =       "",
  year =         "1953",
  pages =        "1144 -- 1156",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Mats70a,
  author =       "H.~Matsuda and H.~Wollnik",
  title =        "The influence of an inhomogeneous magnetic fringing
                 field on the trajectories of charged particles in a
                 third order approximation",
  journal =      "Nuclear Instruments and Methods",
  volume =       "77",
  number =       "",
  month =        "",
  year =         "1970",
  pages =        "40 +",
  referred =     "[Berz91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Mats70b,
  author =       "H.~Matsuda and H.~Wollnik",
  title =        "Third order transfer matrices of the fringing field
                 of an inhomogeneous magnet",
  journal =      "Nuclear Instruments and Methods",
  volume =       "77",
  number =       "",
  month =        "",
  year =         "1970",
  pages =        "283 +",
  referred =     "[Berz91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Mats72a,
  author =       "T.~Matsuo and H.~Matsuda and H.~Wollnik",
  title =        "Particle trajectories in a toroidal condenser in a
                 third order approximation",
  journal =      "Nuclear Instruments and Methods",
  volume =       "103",
  number =       "",
  month =        "",
  year =         "1972",
  pages =        "515 +",
  referred =     "[Berz91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Math89a,
  author =       "MATH",
  title =        "{MATH77}, {Release} 3.0, {A} Library of Mathematical
                 Subprograms for {FORTRAN} 77",
  institution =  "Jet Propulsion Laboratory",
  address =      "Pasadena, CA 91105",
  month =        may,
  year =         "1989",
  type =         "Internal Document",
  number =       "D--134, Rev. B",
  referred =     "[Jued91a]; [Laws91a].",
  note =         "Also available as Program No. NPO--18120 from COSMIC
                 (Computer Software Management and Information Center),
                 The University of Georgia, Athens, GA.",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Mati86a,
  author =       "{\Yu}. V. Matiyasevich",
  title =        "Veshchestvennye chisla i {{\`E}{VM}}",
  journal =      "Kibernetika i Vychislitel'naya Tekhnika",
  volume =       "2",
  number =       "",
  year =         "1986",
  pages =        "104 -- 133",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Mazo91a,
  author =       "Vladimir Mazourik",
  title =        "Integration of Automatic Differentiation into a
                 Numerical Library for {PC}'s",
  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].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Mazu90a,
  author =       "S. I. Mazurik and E. V. Vorozhtsov",
  title =        "Symbolic-numeric computations in the stability
                 analyzes of difference schemes",
  booktitle =    "Proceedings of the 1990 International Symposium on
                 Symbolic and Algebraic Computation",
  year =         "1990",
  editor =       "Shunro Watanabe and Morio Nagata",
  pages =        "177 -- 184",
  publisher =    "Addison-Wesley",
  address =      "Reading, MA",
  referred =     "[Char91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{McCo83a,
  author =       "G. P. McCormick",
  title =        "Nonlinear Programming",
  year =         "1983",
  publisher =    "John Wiley and Sons",
  series =       "",
  address =      "New York",
  referred =     "[Fisc91b].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{McCu43a,
  author =       "W. S. McCulloch and W. Pitts",
  title =        "A logical calculus of ideas immanent in nervous
                 activity",
  journal =      "Bulletin of Mathematical Biophysics",
  volume =       "5",
  number =       "",
  year =         "1943",
  pages =        "115 -- 133",
  referred =     "[Saar91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{McCu69a,
  author =       "J. D. McCully",
  title =        "The {Q} Approach to Problem Solving",
  booktitle =    "Proceedings of FJCC 69",
  publisher =    "AFIPS",
  year =         "1969",
  pages =        "691 -- 699",
  referred =     "[Jued91a]; [Tham91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Mich90a,
  author =       "Leo Michelotti",
  title =        "{MXYZPTLK}: {A} Practical, User-Friendly {C++}
                 Implementation of Differential Algebra: {User}'s
                 Guide",
  institution =  "Fermi National Accelerator Laboratory",
  month =        jan,
  year =         "1990",
  type =         "Technical Memorandum",
  number =       "FN--535",
  address =      "Batavia, IL 60510",
  referred =     "[Jued91a]; [Mich91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Mich91a,
  author =       "Leo Michelotti",
  title =        "{MXYZPTLK}: {A} {C}++ Hacker's Implementation of
                 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 =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Mill75a,
  author =       "W. Miller",
  title =        "Software for roundoff analysis",
  journal =      "ACM Trans. Math. Software",
  year =         "1975",
  volume =       "1",
  number =       "2",
  pages =        "108 -- 128",
  referred =     "[Char91a].",
  comment =      "Char -- good paper.",
  keywords =     "",
  abstract =     "",
}

@Article{Mill88a,
  author =       "G. L. Miller and V. Ramachandran and E. Kaltofen",
  title =        "Efficient parallel evaluation of straight-line code
                 and arithmetic circuits",
  journal =      "SIAM J. Comp.",
  volume =       "17",
  number =       "",
  year =         "1988",
  pages =        "687--695",
  referred =     "[Grie91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Mill75b,
  author =       "W. Miller",
  title =        "Computer search for numerical stability",
  journal =      "J. of the Association for Computing Machinery",
  year =         "1975",
  volume =       "22",
  number =       "",
  pages =        "512 -- 521",
  referred =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Miller:1976:RAD,
  author =       "Webb Miller",
  title =        "Roundoff Analysis by Direct Comparison of Two
                 Algorithms",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "13",
  number =       "3",
  pages =        "382--392",
  month =        jun,
  year =         "1976",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "27 September 2011",
%%%     time            = "17:04:10 MDT",
  bibsource =    "JSTOR database;
                 http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
}

@Book{Mill80a,
  author =       "W. Miller and C. Wrathall",
  title =        "Software for Roundoff Analysis of Matrix Algorithms",
  publisher =    "Academic Press",
  address =      "New York",
  year =         "1980",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "point algorithm; differentiation arithmetic.",
  abstract =     "Chapter 3 of the book describes the concept of a
                 directed graph. It uses the calculation of first order
                 partial derivatives as an example. Roundoff error
                 results are given.",
}

@Book{Mins88a,
  author =       "M. Minsky and S. Papert",
  title =        "Perceptrons, Revised Edition",
  publisher =    "MIT Press",
  series =       "",
  address =      "Cambridge, MA",
  year =         "1988",
  referred =     "[Saar91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Misc{Mona91a,
  author =       "Mike Monagan",
  title =        "Response to electronic mail survey",
  howpublished = "Personal communication",
  month =        mar,
  year =         "1991",
  referred =     "[Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Misc{Mona91b,
  author =       "Mike Monagan",
  title =        "Regarding changes to \protect{\tt optimize} command
                 for future versions of {MAPLE}",
  howpublished = "Personal communication",
  month =        "",
  year =         "1991",
  referred =     "[Char91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Moor66a,
  author =       "Ramon E. Moore",
  title =        "Interval Analysis",
  publisher =    "Prentice-Hall",
  year =         "1966",
  address =      "Englewood Cliffs, NJ",
  referred =     "[Garl85a] \# 967, 969; [Bart70a]; [Chan74a];
                 [Corl82a]; [Corl87a]; [Corl88a]; [Corl91a]; [Gray67a];
                 [Gray74a]; [Hali83a]; [Iri84a]; [Kuba72a]; [Moor79a];
                 [Rall80a]; [Rall81a]; [Yohe79a].",
  comment =      "German translation: {\sl Intervallanalyse,\/}
                 translated by D. Pfaffenzeller, R. Oldenburg,
                 M{\"u}nchen, 1968.",
  keywords =     "boundary value problems; wrapping effect; coordinate
                 transformation; Taylor coefficients.",
  abstract =     "Chapter ten of this book discusses the machine
                 generation of Taylor coefficients. Basic recursion
                 relations are presented.",
}

@Book{Moor79a,
  author =       "Ramon E. Moore",
  title =        "Methods and Applications of Interval Analysis",
  publisher =    "SIAM",
  year =         "1979",
  address =      "Philadelphia, PA",
  referred =     "[Corl87a]; [Corl91a]; [Garl85a] \#980; [Aber88a];
                 [Corl88a]; [Layn91a]; [Neid89a]; [Rall80a]; [Rall81a];
                 [Rall85a]; [Rall91a].",
  comment =      "",
  keywords =     "operator equations; Taylor series; wrapping effect;
                 boundary value problems.",
  abstract =     "Chapter 3 of this book discusses differentiation
                 arithmetic as a recursive iteration. That is, for
                 calculating Taylor coefficients.",
}

@Techreport{Moor79b,
  author =       "R. E. Moore and others",
  title =        "{AIRDOS-EPA}: {A} Computerized Methodology for
                 Estimating Environmental Concentrations and Dose to
                 Man from Airborne Releases of Radionuclides",
  institution =  "Union Carbide Corp., Nucl. Div., Oak Ridge National
                 Laboratory",
  year =         "1979",
  type =         "Technical Report",
  number =       "ORNL-5532",
  address =      "Oak Ridge, TN 37830",
  referred =     "[Horw91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{More90a,
  author =       "Jorge J. Mor\'{e}",
  title =        "On the Performance of Algorithms for Large-Scale
                 Bound Constrained Problems",
  booktitle =    "Large-Scale Numerical Optimization",
  editor =       "T. F. Coleman and Y. Li",
  year =         "1991",
  publisher =    "SIAM",
  pages =        "32 -- 45",
  referred =     "[Bisc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{More80a,
  author =       "Jorge J. Mor\'{e} and B. S. Garbow and K. E.
                 Hillstrom",
  title =        "Implementation guide for {MINPACK}--1",
  institution =  "Mathematics and Computer Sciences Division, Argonne
                 National Laboratory",
  year =         "1980",
  type =         "Technical Report",
  number =       "ANL--80--68",
  address =      "9700 South Cass Ave., Argonne, IL 60439--4801",
  month =        "",
  referred =     "[Bisc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{More80b,
  author =       "Jorge J. Mor\'{e} and B. S. Garbow and K. E.
                 Hillstrom",
  title =        "User guide for {MINPACK}--1",
  institution =  "Mathematics and Computer Sciences Division, Argonne
                 National Laboratory",
  year =         "1980",
  type =         "Technical Report",
  number =       "ANL--80--74",
  address =      "9700 South Cass Ave., Argonne, IL 60439--4801",
  month =        "",
  referred =     "[Bisc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{More81a,
  author =       "Jorge J. Mor\'{e} and Burton S. Garbow and Kenneth E.
                 Hillstrom",
  title =        "Testing unconstrained optimization software",
  journal =      "ACM Trans. Math. Software",
  volume =       "7",
  number =       "1",
  year =         "1981",
  pages =        "17 -- 41",
  referred =     "[Soul91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{More81b,
  author =       "Jorge J. Mor\'{e} and Burton S. Garbow and Kenneth E.
                 Hillstrom",
  title =        "Algorithm 566. {FORTRAN} Subroutines for Testing
                 Unconstrained Optimization Software",
  journal =      "ACM Trans. Math. Software",
  volume =       "7",
  number =       "1",
  year =         "1981",
  pages =        "136 -- 140",
  referred =     "[Gayd91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Morg84a,
  author =       "J. Morgenstern",
  title =        "How to compute fast a function and all its
                 derivatives. {A} variation on the theorem of
                 {Baur}-{Stressen}",
  institution =  "Laboratoire CNRS 168, Universit\'{e} de Nice",
  month =        "",
  year =         "1984",
  type =         "Report",
  number =       "No. 49",
  address =      "Nice, France",
  referred =     "[Tala91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Mori90a,
  author =       "S. Moriguti and Masao Iri and K. Kabaya-Imai",
  title =        "On asymptotic properties of the eigenfunctions of a
                 linear operator",
  journal =      "Japan Journal of Applied Mathematics",
  volume =       "7",
  number =       "",
  year =         "1990",
  pages =        "203 -- 229",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Mort74a,
  author =       "H. S. Morton and J. L. Jenkins and J. N. Blanton",
  title =        "Analytical solutions for {Euler} parameters",
  journal =      "Celestial Mechanics",
  volume =       "10",
  number =       "",
  year =         "1974",
  pages =        "287 -- 301",
  referred =     "[Layn91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Mung90a,
  author =       "Fredrick S. Munger",
  title =        "Applications of Definor Algebra to Ordinary
                 Differential Equations",
  publisher =    "AfterMath Press",
  series =       "",
  address =      "",
  year =         "1990",
  referred =     "",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Book{Muro87a,
  author =       "K. Murota",
  title =        "Systems Analysis by Graphs and Matroids ---
                 {Structural} Solvability and Controllability",
  publisher =    "Springer-Verlag",
  series =       "",
  address =      "",
  year =         "1987",
  referred =     "[Irim91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Muro87b,
  author =       "K. Murota",
  title =        "Menger-decomposition of a graph and its application
                 to the structural analysis of a large-scale system of
                 equations",
  journal =      "Discrete Applied Mathematics",
  volume =       "17",
  number =       "",
  year =         "1987",
  pages =        "",
  referred =     "[Grie91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Muro89a,
  author =       "K. Murota and Koichi Kubota",
  title =        "On Elimination of Intermediate Variables in Fast
                 Automatic Differentiation",
  journal =      "Transactions of Information Processing Society of
                 Japan",
  volume =       "30",
  number =       "",
  year =         "1989",
  pages =        "536 -- 539",
  referred =     "[Kubo91a].",
  note =         "(In Japanese).",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Murt81a,
  author =       "B. A. Murtagh",
  title =        "Advanced Linear Programming: {Computation} and
                 Practice",
  publisher =    "McGraw-Hill",
  series =       "",
  address =      "New York",
  year =         "1981",
  referred =     "[Gayd91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Murt78a,
  author =       "B. A. Murtagh and M. A. Saunders",
  title =        "Large-Scale Linearly Constrained Optimization",
  journal =      "Math. Programming",
  volume =       "14",
  number =       "",
  month =        "",
  year =         "1978",
  pages =        "41 -- 72",
  referred =     "[Gayd91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Murt82a,
  author =       "B. A. Murtagh and M. A. Saunders",
  title =        "A Projected {Lagrangian} Algorithm and Its
                 Implementation for Sparse Nonlinear Constraints",
  journal =      "Math. Programming Study",
  volume =       "16",
  number =       "",
  month =        "",
  year =         "1982",
  pages =        "84 -- 117",
  referred =     "[Gayd91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Murt87a,
  author =       "B. A. Murtagh and M. A. Saunders",
  title =        "{MINOS} 5.1 User's Guide",
  institution =  "Systems Optimization Laboratory, Stanford University",
  month =        "",
  year =         "1987",
  type =         "Technical Report",
  number =       "SOL 83-20R",
  address =      "",
  referred =     "[Gayd91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Phdthesis{Mutr91a,
  author =       "Mark P. W. Mutrie",
  title =        "Towards a Symbolic System for Floating-Point
                 ErrorAnalysis",
  school =       "University of Waterloo",
  year =         "1991",
  referred =     "[Char91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Navo79a,
  author =       "I. Michael Navon and U. Muller",
  title =        "{FESW} --- {A} finite-element {Fortran} {IV} program
                 for solving the shallow water equations",
  journal =      "Advances in Engineering Software",
  year =         "1970",
  volume =       "1",
  number =       "",
  pages =        "77 -- 84",
  month =        "",
  note =         "",
  referred =     "[Bisc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Navo90a,
  author =       "I. Michael Navon and Xiaolei Zou and K. Johnson and
                 J. Derber and J. Sela",
  title =        "Variational Data Assimilation with an Adiabatic
                 Version of the {NMC} Spectral Model",
  journal =      "Monthly Weather Review",
  volume =       "",
  number =       "",
  month =        "",
  year =         "1991",
  note =         "Submitted.",
  pages =        "",
  referred =     "[Navo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Navo90b,
  author =       "I. Michael Navon and Xiaolei Zou and K. Johnson and
                 J. Derber and J. Sela",
  title =        "Variational real-data assimilation with the {N.M.C.}
                 spectral model. {Part I}: {Adiabatic} model tests",
  booktitle =    "Proceedings of the International Symposium on
                 Assimilation of Observations in Meteorology and
                 Oceanography, World Meteorological Organization,
                 Geneva, Switzerland",
  publisher =    "",
  year =         "1990",
  pages =        "341 -- 348",
  referred =     "[Tala91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Navo91a,
  author =       "I. Michael Navon and Xiaolei Zou",
  title =        "Application of the Adjoint Model in Meteorology",
  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 =     "",
}

@Techreport{Neid87a,
  author =       "Richard D. Neidinger",
  title =        "Automatic Differentiation and {APL}",
  type =         "Lecture Notes",
  institution =  "Davidson College",
  address =      "Davidson, NC 28036",
  year =         "1987",
  referred =     "",
  comment =      "",
  keywords =     "differentiation arithmetic; APL; computer program.",
  abstract =     "The lecture notes discuss implementing
                 differentiation arithmetic in APL. APL programs which
                 implement the basic ideas of differentiation
                 arithmetic are given. Pascal's triangle is a standard
                 feature of APL which allows the binomial coefficients
                 required to be found using a table lookup.",
}

@Article{Neid89a,
  author =       "Richard D. Neidinger",
  title =        "Automatic Differentiation and {APL}",
  journal =      "College Mathematics Journal",
  volume =       "20",
  number =       "3",
  year =         "1989",
  pages =        "238 -- 251",
  referred =     "[Flan91a]; [Kalm91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Neid90a,
  author =       "Richard D. Neidinger",
  title =        "An Efficient Method for the Numerical Evaluation of
                 Partial Derivatives of Arbitrary Order",
  type =         "Preprint",
  institution =  "Davidson College",
  address =      "Davidson, NC 28036",
  year =         "1990",
  referred =     "[Jued91a]; [Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Neidinger:1992:EMN,
  author =       "Richard D. Neidinger",
  title =        "An Efficient Method for the Numerical Evaluation of
                 Partial Derivatives of Arbitrary Order",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "159--173",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "http://doi.acm.org/10.1145/146847.146924",
  ISSN =         "0098-3500",
  MRclass =      "65D25 (65Y10)",
  MRnumber =     "93b:65040",
  bibdate =      "Mon Sep 05 08:48:51 1994",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p159-neidinger/",
  abstract =     "For any typical multivariable expression $f$, point
                 $a$ in the domain of $f$, and positive integer
                 maxorder, this method produces the numerical values of
                 all partial derivatives at $a$ up through order
                 maxorder. By the technique known as automatic
                 differentiation, theoretically exact results are
                 obtained using numerical (as opposed to symbolic)
                 manipulation. The key ideas are a hyperpyramid data
                 structure and a generalized Leibniz's rule. Any
                 expression in $n$ variables corresponds to a
                 hyperpyramid array, in $n$-dimensional space,
                 containing the numerical values of all unique partial
                 derivatives (not wasting space on different
                 permutations of derivatives). The arrays for simple
                 expressions are combined by hyperpyramid operators to
                 form the arrays for more complicated expressions. These
                 operators are facilitated by a generalized Leibniz's
                 rule which, given a product of multivariable functions,
                 produces any partial derivative by forming the minimum
                 number of products (between two lower partials)
                 together with a product of binomial coefficients. The
                 algorithms are described in abstract pseudo-code. A
                 section on implementation shows how these ideas can be
                 converted into practical and efficient programs in a
                 typical computing environment. For any specific
                 problem, only the expression itself would require
                 recoding.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf I.1.2}: Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Nonalgebraic algorithms. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Numerical algorithms. {\bf G.4}: Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, Algorithm
                 analysis. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Efficiency.",
}

@Inproceedings{Nged79a,
  author =       "Edward W. Ng",
  title =        "Symbolic-numeric interface: {A} review",
  booktitle =    "{EUROSAM 79, Colloque International sur les
                 M\'{e}thodes de Calcul Symbolique et Alg\'{e}brique}",
  year =         "1979",
  editor =       "Edward W. Ng",
  pages =        "330 -- 345",
  organization = "{EUROSAM, Marseille, France}",
  publisher =    "Springer-Verlag",
  address =      "New York",
  month =        jun,
  referred =     "[Char91a].",
  comment =      "Char -- Summary of various applications.",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Nged79b,
  author =       "E. Ng and Bruce W. Char",
  title =        "Gradient and {Jacobian} computation for numerical
                 applications",
  booktitle =    "Proceedings of the 1979 Macsyma User's Conference",
  year =         "1979",
  editor =       "V. Ellen Golden",
  pages =        "604 -- 621",
  organization = "{NASA, Washington, DC}",
  month =        jun,
  referred =     "[Char91a].",
  comment =      "Char -- Optimization techniques.",
  keywords =     "",
  abstract =     "",
}

@Book{Nije78a,
  author =       "A. Nijenhuis and H. S. Wilf",
  title =        "Combinatorial Algorithms",
  edition =      "Second",
  publisher =    "Academic Press",
  series =       "",
  address =      "New York",
  year =         "1978",
  referred =     "[Flan91a]; [Laws91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Techreport{NOC76a,
  author =       "N. O. C.",
  title =        "{OPTIMA} - {Routines} for Optimisation Problems",
  type =         "{Technical} {Report}",
  number =       "",
  institution =  "The Numerical Optimisation Center, Hatfield
                 Polytechnic",
  address =      "Hatfield, UK",
  year =         "1976",
  referred =     "[Garc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Noce80a,
  author =       "J. Nocedal",
  title =        "Updating Quasi-{Newton} Matrices with Limited
                 Storage",
  journal =      "Mathematics of Computation",
  volume =       "35",
  number =       "",
  month =        "",
  year =         "1980",
  pages =        "773 -- 782",
  referred =     "[Navo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Mastersthesis{Nola53a,
  author =       "J. F. Nolan",
  title =        "Analytical Differentiation on a Digital Computer",
  school =       "Massachusetts Institute of Technology",
  year =         "1953",
  month =        may,
  referred =     "[Char91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Oblo78a,
  author =       "E. M. Oblow",
  title =        "Sensitivity Theory for Reactor Thermal-Hydraulics
                 Problems",
  journal =      "Nucl. Sci. Eng.",
  volume =       "68",
  number =       "",
  month =        "",
  year =         "1978",
  pages =        "322",
  referred =     "[Worl91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Oblo83a,
  author =       "E. M. Oblow",
  title =        "An Automated Procedure for Sensitivity Analysis Using
                 Computer Calculus",
  institution =  "Union Carbide Corp., Nucl. Div., Oak Ridge National
                 Laboratory",
  address =      "Oak Ridge, Tennessee",
  year =         "1985",
  type =         "",
  number =       "ORNL/TM-8776",
  referred =     "[Horw91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Oblo85a,
  author =       "E. M. Oblow",
  title =        "{GRESS}: {Gradient}-enhanced software system.
                 {Version} {D} User's guide",
  institution =  "Oak Ridge National Laboratory",
  address =      "Oak Ridge, Tennessee",
  year =         "1985",
  referred =     "",
  comment =      "This is a user's guide to a package which
                 incorporates differentiation arithmetic.",
  keywords =     "Differentiation arithmetic; computer program;
                 sensitivity analysis; preprocessor.",
  abstract =     "This describes a Fortran precompiler which takes as
                 input Fortran programs. These are then differentiated
                 using differentiation arithmetic techniques. The
                 output is a Fortran subroutine which will calculate
                 the value of the Jacobian of a function without using
                 finite differencing. The packages main application is
                 in the area of sensitivity analysis.",
}

@Article{Oblo86a,
  author =       "E. M. Oblow and F. G. Pin and R. Q. Wright",
  title =        "Sensitivity Analysis Using Computer Calculus: {A}
                 Nuclear Waste Application",
  journal =      "Nucl. Sci. Eng.",
  volume =       "94",
  number =       "46",
  year =         "1986",
  pages =        "",
  referred =     "[Horw91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{ONei71a,
  author =       "R. O'Neill",
  title =        "Algorithm {AS47} - {Function} minimization using a
                 simplex procedure",
  journal =      "Applied Statistics",
  volume =       "20, 23, 25",
  number =       "",
  year =         "1971",
  pages =        "338 -- 346, 250 -- 252, 97",
  referred =     "[Garc91a].",
  keywords =     "",
  abstract =     "",
}

@Article{Ostr71a,
  author =       "G. M. Ostrovskii and {\Ju}. M. Wolin and W. W.
                 Borisov",
  title =        "{\"U}ber die {Berechnung} von {Ableitungen}",
  journal =      "Wissenschaftliche Zeitschrift der Technischen
                 Hochschule f{\"u}r Chemie, Leuna-Merseburg",
  volume =       "13",
  number =       "4",
  month =        "",
  year =         "1971",
  pages =        "382 -- 384",
  referred =     "[Voli85a].",
  comment =      "This is a description of a program for automatic
                 derivative computation.",
  keywords =     "differentiation arithmetic; back method; computer
                 program.",
  abstract =     "",
}

@Article{Pant88a,
  author =       "C. C. Pantelides",
  title =        "{SPEEDUP} Recent Advances in Process Simulation",
  journal =      "Comput. Chem. Engin.",
  volume =       "12",
  number =       "",
  year =         "1988",
  pages =        "745 -- 755",
  referred =     "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Park90a,
  author =       "S. C. Parkhurst",
  title =        "The Evaluation of Exact Numerical {Jacobians} using
                 Automatic Differentiation",
  type =         "Technical Report",
  number =       "NOC TR224",
  institution =  "The Numerical Optimisation Center, Hatfield
                 Polytechnic",
  address =      "Hatfield, UK",
  month =        dec,
  year =         "1990",
  referred =     "[Dixo91a].",
  comment =      "Presented at The Eleventh Conference on Differential
                 Equations, Dundee University, July 1990.",
  keywords =     "",
  abstract =     "",
}

@Book{Parl80a,
  author =       "P. Parlett",
  title =        "The Symmetric Eigenvalue Problem",
  publisher =    "Prentice-Hall",
  series =       "Series in Computational Mathematics",
  address =      "Englewood Cliffs, NJ",
  year =         "1980",
  referred =     "[Tala91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Pask67a,
  author =       "{\Ye}. N. Paskhin",
  title =        "Analytic function differentiation by computer",
  journal =      "Computer Methods and Programming",
  volume =       "9",
  year =         "1967",
  pages =        "",
  referred =     "[Voli85a].",
  note =         "(In Russian).",
  comment =      "",
  keywords =     "point algorithm; symbolic algebra; program
                 transformation.",
  abstract =     "",
}

@Article{Pave85a,
  author =       "Richard Pavelle and Paul S. Wang",
  title =        "{MACSYMA} from {F} to {G}",
  journal =      "Journal of Symbolic Computation",
  volume =       "1",
  number =       "1",
  month =        mar,
  year =         "1985",
  pages =        "69 -- 100",
  referred =     "[Char91a]; [Gold91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Peac55a,
  author =       "D. W. Peaceman and H. H. {Rachford, Jr.}",
  title =        "The Numerical Solution of Parabolic and Elliptic
                 Differential Equations",
  journal =      "J. of SIAM",
  volume =       "3",
  number =       "1",
  month =        "",
  year =         "1955",
  pages =        "28 -- 41",
  referred =     "[Shah91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Pene76a,
  author =       "V. V. Penenko and N. N. Obraztsov",
  title =        "A Variational Initialization Method for the Fields of
                 the Meteorological Elements",
  journal =      "Meteorol. Gidrol. (Soviet Meteorol. Hydrol.)",
  volume =       "11",
  number =       "",
  month =        "",
  year =         "1976",
  pages =        "1 -- 11",
  referred =     "[Navo91a].",
  note =         "(English translation).",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Pfei80a,
  author =       "F. W. Pfeiffer",
  title =        "Some Advances Related to Nonlinear Programming",
  journal =      "SIGMAP Bulletin",
  volume =       "",
  number =       "",
  year =         "1980",
  month =        jan,
  pages =        "1 -- 7",
  referred =     "[Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Pfei87a,
  author =       "F. W. Pfeiffer",
  title =        "Automatic differentiation in {PROSE}",
  journal =      "ACM SIGNUM Newsletter",
  volume =       "22",
  number =       "1",
  year =         "1987",
  pages =        "1 -- 8",
  referred =     "[Jued91a]; [Tham91a].",
  comment =      "",
  keywords =     "point algorithm; differentiation arithmetic; program
                 transformation.",
  abstract =     "A programming language is presented in which has the
                 feature that first and second order partial
                 derivatives of a function can be calculated using
                 differentiation arithmetic. The language syntax allows
                 the user to specify which variables each function is
                 required to be differentiated with respect to. Model
                 examples are provided.",
}

@Incollection{Plas90a,
  author =       "Paul E. Plassmann",
  title =        "Sparse {Jacobian} estimation and factorization on a
                 multiprocessor",
  booktitle =    "Large-Scale Optimization",
  year =         "1990",
  editor =       "T. F. Coleman and Y. Li",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "152 -- 179",
  referred =     "[Bisc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Pohl89a,
  author =       "Ira Pohl",
  title =        "{C}++ for Programmers",
  publisher =    "Benjamin/Cummings",
  series =       "",
  address =      "Redwood City, CA",
  year =         "1989",
  referred =     "[Kalm91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Book{Pres86a,
  author =       "W. H. Press and B. P. Flannery and S. A. Teukolsky
                 and W. T. Vetterling",
  title =        "Numerical Recipes: {The} Art of Scientific Computing",
  publisher =    "Cambridge University Press",
  series =       "",
  address =      "New York",
  year =         "1986",
  referred =     "[Layn91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

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

@Techreport{Pryc87a,
  author =       "John D. Pryce and Paul H. Davis",
  title =        "A New Implementation of Automatic Differentiation for
                 Use with Numerical Software",
  institution =  "Mathematics Department, Bristol University",
  month =        "",
  year =         "1987",
  type =         "Technical Report",
  number =       "TR AM-87-11",
  address =      "",
  referred =     "[Dixo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Manual{PROS77a,
  author =       "",
  title =        "{PROSE} -- {A} General Purpose Higher Level Language",
  organization = "Control Data Corporation",
  note =         "Procedure Manual (Pub. No. 84003000 Rev. B), Calculus
                 Operations Manual (Pub. No. 84003200 Rev. A), Calculus
                 Applications Guide (Pub. No. 84000170 Rev A).",
  address =      "",
  year =         "1977",
  referred =     "[Jued91a]; [Tham91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Manual{Radi91a,
  author =       "{Radiation Shielding}",
  title =        "{GRESS} 1.0, Gradient Enhanced Software System",
  organization = "distributed by Radiation Shielding Information
                 Center, PSR-231",
  address =      "",
  year =         "1991",
  referred =     "[Worl91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Book{Rall79a,
  author =       "Louis B. Rall",
  title =        "Computational Solution of Nonlinear Operator
                 Equations",
  publisher =    "Wiley, Krieger",
  series =       "",
  address =      "",
  year =         "1969, 1979",
  referred =     "[Rall91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

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

@Book{Rall81a,
  author =       "Louis B. Rall",
  title =        "Automatic Differentiation: {Techniques} and
                 Applications",
  publisher =    "Springer-Verlag",
  year =         "1981",
  volume =       "120",
  series =       "Lecture Notes in Computer Science",
  address =      "Berlin",
  referred =     "[Garl85a] \# 1243; [Arbe85a]; [Carl86a]; [Carl86b];
                 [Carl86c]; [Chan86a]; [Corl82a]; [Corl87a]; [Corl88a];
                 [Corl91a]; [Dixo87a]; [Dixo91a]; [Fisc87a]; [Fisc91b];
                 [Garc91a]; [Hali83a]; [Hill82a]; [Irim84a]; [Irim91a];
                 [Jued91a]; [Kagi86a]; [Layn91a]; [Mazo91a]; [Neid89a];
                 [Pfei87a]; [Rall84a]; [Rall85a]; [Rall87a]; [Rall91a];
                 [Tesf91a]; [Voli85a]; [Wexl87a].",
  comment =      "Contains all the details about how to do automatic
                 differentiation and surveys application to ordinary
                 differential equations.",
  keywords =     "automatic differentiation.",
  abstract =     "Rall gives complete details on algorithms for the
                 generation and differentiation of code lists for
                 expressions. Recurrence relations for Taylor
                 coefficients are given. Applications to ordinary
                 differential equations, quadrature, optimization, and
                 other problems are given.",
}

@Incollection{Rall83a,
  author =       "Louis B. Rall",
  title =        "Differentiation and generation of {Taylor}
                 coefficients in {Pascal}-{SC}",
  booktitle =    "A New Approach to Scientific Computation",
  publisher =    "Academic Press",
  address =      "New York",
  editor =       "Ulrich W. Kulisch and Willard L. Miranker",
  year =         "1983",
  pages =        "291 -- 309",
  referred =     "CR 8411 0945; [Garl85a] \# 1252; [Carl86a];
                 [Carl86b]; [Carl86c]; [Layn91a]; [Pfei87a]; [Rall85a];
                 [Rall87a]; [Rall91a].",
  comment =      "Also appeared as {\sl MRC Technical Summary Report
                 No. 2452,\/} Mathematics Research Center, University
                 of Wisconsin - Madison (1982).",
  keywords =     "differentiation arithmetic.",
  abstract =     "",
}

@Article{Rall83b,
  author =       "Louis B. Rall",
  title =        "Mean value and {Taylor} forms in interval analysis",
  journal =      "SIAM J. Math. Anal.",
  volume =       "2",
  number =       "",
  year =         "1983",
  pages =        "",
  referred =     "[Rall91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Rall84a,
  author =       "Louis B. Rall",
  title =        "Differentiation in {Pascal}-{SC}: {Type} {GRADIENT}",
  journal =      "ACM Trans. Math. Software",
  volume =       "10",
  number =       "2",
  publisher =    "",
  month =        jun,
  year =         "1984",
  pages =        "161 -- 184",
  referred =     "[Arbe85a]; [Carl86a]; [Fisc87a]; [Gold91a];
                 [Kalm91a]; [Neid87a]; [Rall87a]; [Tesf91a].",
  comment =      "Also appeared as {\sl MRC Technical Summary Report
                 No. 2400,\/} Mathematics Research Center, University
                 of Wisconsin-Madison (1982).",
  keywords =     "point algorithm; differentiation arithmetic.",
  abstract =     "The author shows how first order parital derivatives
                 can be generated automatically using the language
                 PASCAL--SC. The form data structures used in the
                 language are given, as well as the source code. The
                 resulting code is tested on the solution of nonlinear
                 systems of equations using Newton's method. The
                 numerical example given is a simple 4 variable
                 problem.",
}

@Article{Rall86a,
  author =       "Louis B. Rall",
  title =        "The arithmetic of differentiation",
  journal =      "Mathematics Magazine",
  volume =       "59",
  publisher =    "5",
  month =        dec,
  year =         "1986",
  pages =        "275 -- 282",
  referred =     "[Kalm91a]; [Mich91a]; [Neid87a]; [Neid89a];
                 [Rall87a]; [Tesf91a].",
  comment =      "Also appeared as {\sl MRC Technical Summary Report
                 No. 2688,\/} Mathematics Research Center, University
                 of Wisconsin-Madison.",
  keywords =     "differentiation arithmetic; groups; rings.",
  abstract =     "The author discusses differentiation of a scalar
                 function. He formulates this as arithmetic on a
                 two-tuple containing the value of the function and the
                 value of the derivative of the function. The
                 arithmetic formed is shown to have various group and
                 ring properties. A second formulation similar to that
                 for complex arithmetic using $ z = x+iy $ is also
                 discussed. The initial system setup is shown to work
                 on a very simple example run on a programmable hand
                 calculator.",
}

@Techreport{Rall85a,
  author =       "Louis B. Rall",
  title =        "Global optimisation using automatic differentiation
                 and interval arithmetic",
  type =         "Technical Summary Report",
  number =       "No. 2832",
  institution =  "Mathematics Research Center, University of Wisconsin
                 - Madison",
  year =         "1985",
  pages =        "",
  referred =     "[Pric87a].",
  comment =      "",
  keywords =     "Global constrained optimisation; differentiation
                 arithmetic; interval iteration; numerical examples.",
  abstract =     "Using differentiation arithmetic, algorithms are
                 presented for finding one or all of the critical
                 points of a twice differentiable function. These
                 methods use interval iterations in the given
                 (rectangular) region. Guaranteed bounds are also given
                 for all of the quantities of interest. The
                 n-dimensional Rosenbrock function is used as the test
                 problem.",
}

@Incollection{Rall87a,
  author =       "Louis B. Rall",
  title =        "Optimal implementation of differentiation arithmetic",
  booktitle =    "Computerarithmetic",
  publisher =    "Teubner, B. G.",
  address =      "Stuttgart",
  editor =       "Edgar W. Kaucher and Ulrich W. Kulisch and Christian
                 Ullrich",
  year =         "1987",
  pages =        "287 -- 295",
  referred =     "",
  comment =      "In [Kauc87a]. Also appeared as {\sl MRC Technical
                 Summary Report No. 2920,\/} Mathematics Research
                 Center, University of Wisconsin-Madison (1986).",
  keywords =     "differentiation arithmetic.",
  abstract =     "The concepts of differentiation arithmetic are
                 compared with real arithmetic, complex arithmetic and
                 general computer arithmetic. The implementation of
                 differentiation arithmetic is looked at in an optimal
                 way, in the context of roundoff errors, for both
                 partial derivatives and Taylor coefficients.",
}

@Incollection{Rall90a,
  author =       "Louis B. Rall",
  title =        "Differentiation Arithmetics",
  booktitle =    "Computer Arithmetic and Self-Validating Numerical
                 Methods",
  year =         "1990",
  editor =       "Christian Ullrich",
  publisher =    "Academic Press",
  address =      "New York",
  pages =        "73 -- 90",
  referred =     "[Rall91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Rall91a,
  author =       "Louis B. Rall",
  title =        "Point and Interval Differentiation Arithmetics",
  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 =     "",
}

@Article{Rall71a,
  author =       "Louis B. Rall and G. Wanner",
  title =        "Experience with {Lie} series",
  journal =      "Meth. und Verfahren der Math. Physik",
  volume =       "5",
  year =         "1971",
  pages =        "29 -- 42",
  referred =     "[Rall80a].",
  comment =      "",
  keywords =     "point algorithm; automatic differentiation; Lie
                 series.",
  abstract =     "",
}

@Book{Rats84a,
  author =       "H. Ratschek and J. Rokne",
  title =        "Computer Methods for the Range of Functions",
  publisher =    "Halsted Press, Wiley",
  series =       "",
  address =      "New York",
  year =         "1984",
  referred =     "[Rall91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Reit65a,
  author =       "Alan Reiter",
  title =        "Automatic generation of Taylor coefficients
                 {(TAYLOR)}",
  type =         "Prog. 3",
  institution =  "Mathematics Research Center, University of
                 Wisconsin-Madison",
  year =         "1965",
  pages =        "",
  referred =     "[Rall80a]; [Rall81a].",
  comment =      "",
  keywords =     "automatic differentiation; Taylor coefficients.",
  abstract =     "",
}

@Techreport{Reit65b,
  author =       "Alan Reiter",
  title =        "Compiler of differential expressions {(CODEX)}",
  type =         "Research Program Note",
  number =       "3",
  institution =  "Mathematics Research Center, University of
                 Wisconsin-Madison",
  pages =        "",
  year =         "1965",
  abstract =     "",
  comment =      "",
  keywords =     "precompiler.",
  referred =     "[Rall80a].",
}

@Techreport{Reit67a,
  author =       "Alan Reiter",
  title =        "Automatic generation of Taylor coefficients
                 {(TAYLOR)} for the {CDC} 1604",
  type =         "Technical Summary Report",
  number =       "No. 830",
  institution =  "Mathematics Research Center, University of Wisconsin
                 - Madison",
  year =         "1967",
  pages =        "",
  referred =     "[Garl85a] \# 1317; [Hali83a]; [Rall80a]; [Rall81a].",
  comment =      "",
  keywords =     "automatic differentiation; Taylor coefficients;
                 computer program.",
  abstract =     "This is a CDC 1604 program which computes the series
                 expansion of a function with respect to one variable.
                 The basic theoretical results used are given are well
                 as a listing of the program.",
}

@Book{Ritt50a,
  author =       "J. F. Ritt",
  title =        "Differential Algebra",
  publisher =    "American Mathematical Society",
  series =       "",
  address =      "Washington, DC",
  year =         "1950",
  referred =     "[Berz91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Rose78a,
  author =       "D. J. Rose and R. E. Tarjan",
  title =        "Data Structures and Network Algorithms",
  journal =      "SIAM J. A. M.",
  volume =       "34",
  number =       "",
  year =         "1978",
  pages =        "177 -- 197",
  referred =     "[Grie91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Rose63a,
  author =       "F.  Rosenblatt",
  title =        "Principles of Neurodynamics",
  publisher =    "Spartan",
  series =       "",
  address =      "New York",
  year =         "1963",
  referred =     "[Saar91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Misc{Rost91b,
  author =       "Nicole Rostaing",
  title =        "",
  howpublished = "Poster presented at {SIAM} {Workshop} on {Automatic}
                 {Differentiation}, {Breckenridge}, {CO}",
  month =        jan,
  year =         "1991",
  referred =     "[Char91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Misc{Rost91a,
  author =       "Nicole Rostaing and M. Gaetano",
  title =        "Response to electronic mail survey",
  howpublished = "Personal communication",
  month =        mar,
  year =         "1991",
  referred =     "[Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Rote90a,
  author =       "G. Rote",
  title =        "Path problems in graphs",
  booktitle =    "Computational Graph Theory",
  year =         "1990",
  editor =       "",
  publisher =    "Springer-Verlag",
  address =      "Berlin",
  series =       "Computing Supplementum 7",
  pages =        "155 -- 189",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Rume86a,
  author =       "David E. Rumelhart and James L. McClelland and {the
                 PDP Research Group}",
  title =        "Parallel Distributed Processing. Explorations in the
                 Microstructure of Cognition",
  publisher =    "MIT Press",
  series =       "",
  address =      "",
  year =         "1986",
  referred =     "[Saar91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Saar91a,
  author =       "Sirpa Saarinen and Randall Bramley and George
                 Cybenko",
  title =        "Neural Networks, Backpropagation, and 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 =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Saarinen:1991:NSN,
  author =       "Sirpa Saarinen and R. Bramley and George Cybenko",
  title =        "The numerical solution of neural network training
                 problems",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "",
  number =       "",
  pages =        "",
  month =        "????",
  year =         "1991",
  CODEN =        "SIJCD4",
  ISSN =         "0196-5204",
  bibdate =      "Wed Jun 29 08:32:40 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
  note =         "Submitted. Issued as CSRD Technical Report No. 1089.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  referred =     "[Saar91a].",
}

@Article{Sawy84a,
  author =       "J. W. {Sawyer, Jr.}",
  title =        "First partial differentiation by computer with an
                 application to categorical data analysis",
  journal =      "The American Statistician",
  volume =       "38",
  number =       "",
  year =         "1984",
  pages =        "300 -- 308",
  referred =     "[Irim91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Sela80a,
  author =       "J. G. Sela",
  title =        "Spectral Modeling at the {National} {Meteorological}
                 {Center}",
  journal =      "Monthly Weather Review",
  volume =       "108",
  number =       "",
  month =        "",
  year =         "1980",
  pages =        "1279 -- 1292",
  referred =     "[Navo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Phdthesis{Shah76a,
  author =       "Piyush C.  Shah",
  title =        "Estimation of Properties in Petroleum Reservoirs",
  school =       "California Institute of Technology",
  address =      "",
  month =        "",
  year =         "1976",
  referred =     "[Shah91a].",
  note =         "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Shah91a,
  author =       "Piyush Shah",
  title =        "Application of Adjoint Equations to Estimation of
                 Parameters in Distributed Dynamic Systems",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  year =         "1991",
  editor =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "",
  referred =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Skee89a,
  author =       "R. D. Skeel",
  title =        "Safety in Numbers: {The} Boundless Errors of
                 Numerical Computation",
  institution =  "Department of Energy",
  year =         "1989",
  type =         "Report",
  number =       "ER/25026--30",
  address =      "",
  referred =     "[Layn91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Soul86a,
  author =       "Edgar J. Souli\'{e}",
  title =        "L'am\'{e}lioration de l'orbite d'une \'{e}toile
                 double visuelle",
  journal =      "Astronomy and Astrophysics",
  volume =       "164",
  number =       "",
  year =         "1986",
  pages =        "408 -- 414",
  referred =     "[Soul91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Soul88a,
  author =       "Edgar J. Souli\'{e}",
  title =        "A few examples of least squares optimization in
                 physical chemistry and astronomy",
  booktitle =    "Trends in Mathematical Optimization",
  year =         "1988",
  editor =       "K.-H. Hoffmann and J. B. Hiriart-Urruty and C.
                 Lemar\'{e}chal and J.  Zowe",
  publisher =    "Birkhauser Verlag",
  address =      "Basel",
  pages =        "327 -- 340",
  referred =     "[Soul91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Soul89a,
  author =       "Edgar J. Souli\'{e} and Pierre C. Lesieur",
  title =        "Quantitative analysis of the electron paramagnetic
                 resonance spectrum of a {Uranium(III)} compound",
  journal =      "J. Chem. Soc., Faraday Trans. 1",
  volume =       "85",
  number =       "12",
  year =         "1989",
  pages =        "4053 -- 4062",
  referred =     "[Soul91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Soul91a,
  author =       "Edgar J. Souli\'{e}",
  title =        "User's Experience with {Fortran} Precompilers for
                 Least Squares Optimization Problems",
  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 =     "",
}

@Phdthesis{Spee80a,
  author =       "B. Speelpenning",
  title =        "Compiling Fast Partial Derivatives of Functions Given
                 by Algorithms",
  school =       "Department of Computer Science, University of
                 Illinois at Urbana-Champaign",
  month =        jan,
  year =         "1980",
  address =      "Urbana-Champaign, IL 61801",
  referred =     "[Arbe85a]; [Corl91a]; [Gayd91a]; [Irim91a];
                 [Jued91a]; [Kubo91a]; [Hali83a]; [Hill82a]; [Pfei87a];
                 [Rall91a]; [Tesf91a]; [Thac91a].",
  comment =      "Char -- good stuff",
  keywords =     "point algorithm; precompiler; numerical results.",
  abstract =     "This is the author's doctoral thesis. It starts by
                 comparing previous work in the area of symbolic
                 differentiation of algorithms. Specifically it
                 considers the work of Warner in 1975, Joss in 1976 and
                 Kedem in 1977. The conclusions reached in this
                 discussion are that the work by Joss is the best in
                 terms of improvement. The author proceeds to describe
                 how Joss' work can be improved in terms of speed,
                 accuracy and space. A package, Jake, is described
                 which is a compiler that takes a Fortran 66 input
                 definition of a function. This input is limited in
                 that only one subroutine can be specified, and that
                 certain Fortran 66 statements are disallowed. Jake is
                 instructed on how to perform its task by directives
                 within the subroutine. Timing results are provided on
                 the performance of the code produced by Jake over
                 those where finite differencing is used.",
}

@Book{Stac74a,
  author =       "W. M. Stacey",
  title =        "Variational Methods in Nuclear Reactor Physics",
  publisher =    "Academic Press",
  series =       "",
  address =      "New York",
  year =         "1974",
  referred =     "[Worl91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Stei86a,
  author =       "Stanly Steinberg and Patrick J. Roache",
  title =        "Using {Macsyma} to Write {FORTRAN} Subroutines",
  journal =      "Journal of Symbolic Computation",
  year =         "1986",
  pages =        "213 -- 216",
  month =        jun,
  volume =       "2",
  number =       "2",
  referred =     "[Char91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Step87a,
  author =       "Bruce R. Stephens and John D. Pryce",
  title =        "Passing functions in {Fortran} for automatic
                 differentiation",
  type =         "Technical Report",
  number =       "{AM}--87--13",
  institution =  "Maths. Dept., Bristol University",
  address =      "Bristol, UK",
  year =         "1987",
  referred =     "",
  comment =      "",
  keywords =     "precompiler.",
  abstract =     "This is a survey of possible methods for passing a
                 function defined by a high level language procedure to
                 an automatic differentiation package. The automatic
                 differentiation package described in [Davi87a] is
                 specifically considered.",
}

@Manual{Step90a,
  author =       "Bruce R. Stephens and John D. Pryce",
  title =        "The {DAPRE/UNIX} Preprocessor Users' Guide v1.2",
  organization = "Royal Military College of Science at Shrivenham",
  year =         "1990",
  referred =     "[Corl91a]; [Soul91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Step91a,
  author =       "Bruce R. Stephens and John D. Pryce",
  title =        "{DAPRE}: {A} Differentiation Arithmetic System for
                 {FORTRAN}",
  institution =  "Royal Military College of Science",
  year =         "1991",
  type =         "Technical Report",
  number =       "ACM--91--3",
  address =      "Shrivenham, UK",
  referred =     "[Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Stet86a,
  author =       "Hans J. Stetter",
  title =        "Algorithms for the Inclusion of Solutions of Ordinary
                 Initial Value Problems",
  booktitle =    "Equadiff 6: {Proceedings} of the International
                 Conference on Differential Equations and Their
                 Applications (Brno, 1985)",
  year =         "1986",
  editor =       "Jaram\'{i}r Vosmansk\'{y} and Milo\u{o}s Zl\'{a}mal",
  publisher =    "Springer-Verlag",
  series =       "Lecture Notes in Mathematics",
  volume =       "1192",
  pages =        "85 -- 94",
  address =      "Berlin",
  referred =     "[Corl91a].",
}

@Incollection{Stet90a,
  author =       "Hans J. Stetter",
  title =        "Validated solution of initial value problems for
                 {ODEs}",
  booktitle =    "Computer Arithmetic and Self-Validating Numerical
                 Methods",
  year =         "1990",
  editor =       "Christian Ullrich",
  publisher =    "Academic Press",
  address =      "New York",
  pages =        "171 -- 187",
  referred =     "[Layn91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Stou77a,
  author =       "David R. Stoutemyer",
  title =        "Automatic Error Analysis Using Computer Algebraic
                 Manipulation",
  journal =      "ACM Trans. Math. Software",
  year =         "1977",
  volume =       "3",
  number =       "1",
  pages =        "26 -- 43",
  month =        mar,
  referred =     "[Char91a].",
  comment =      "Char -- Automatic error analysis in REDUCE.",
  keywords =     "",
  abstract =     "",
}

@Book{Stro86a,
  author =       "Bjarne Stroustrup",
  title =        "The {C++} Programming Language",
  publisher =    "Addison-Wesley",
  year =         "1986",
  address =      "Reading, MA",
  referred =     "[Corl91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Manual{STSC89a,
  author =       "STSC",
  title =        "{APL*PLUS} System for the {PC} - {User}'s Manual",
  organization = "STSC, Inc.",
  address =      "Rockville, MD",
  year =         "1988",
  referred =     "[Garc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Tala91a,
  author =       "Oliver Talagrand",
  title =        "The Use of Adjoint Equations in Numerical Modelling
                 of the Atmospheric Circulation",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  year =         "1991",
  editor =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "",
  referred =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Tala87a,
  author =       "Olivier Talagrand and P. Courtier",
  title =        "Variational Assimilation of Meteorological
                 Observations with the Adjoint Vorticity Equation --
                 {Part} {I}. {Theory}",
  journal =      "Q. J. R. Meteorol. Soc.",
  volume =       "113",
  number =       "",
  month =        "",
  year =         "1987",
  pages =        "1311 -- 1328",
  referred =     "[Navo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Tesf91a,
  author =       "Leigh Tesfatsion",
  title =        "Automatic Evaluation of Higher-Order Partial
                 Derivatives for Nonlocal Sensitivity Analysis",
  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 =     "[Dixo91a]; [Jued91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Thac66a,
  author =       "H. C. {Thacher, Jr.}",
  title =        "Solution of transcendental equations by series
                 reversion",
  journal =      "Comm. ACM",
  volume =       "9",
  number =       "1",
  year =         "1966",
  pages =        "10 -- 11",
  referred =     "[Laws91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Thac90a,
  author =       "William Carlisle Thacker",
  title =        "Large least-squares problems and the need for
                 automating the generation of adjoint codes",
  booktitle =    "Computational Solution of Nonlinear Systems of
                 Equations",
  year =         "1990",
  editor =       "",
  publisher =    "American Mathematical Society",
  address =      "",
  series =       "Lectures in Applied Mathematics, No. 26",
  pages =        "645 -- 677",
  referred =     "[Thac91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Thac91a,
  author =       "William Carlisle Thacker",
  title =        "Automatic Differentiation from an Oceanographer's
                 Perspective",
  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 =     "",
}

@Article{Thac88a,
  author =       "William Carlisle Thacker and R. B. Long",
  title =        "Fitting Dynamics to Data",
  journal =      "J. Geophys. Res.",
  volume =       "93",
  number =       "C2",
  year =         "1988",
  pages =        "1227 -- 1240",
  referred =     "[Horw91a]; [Irim91a]; [Tala91a]; [Thac91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Tham69a,
  author =       "Joseph M. Thames",
  title =        "{SLANG}, A Problem-Solving Language for
                 Continuous-Model Simulation and Optimization",
  booktitle =    "Proceedings of the ACM 24th National Conf.",
  publisher =    "ACM",
  year =         "1969",
  pages =        "",
  referred =     "[Jued91a]; [Tham91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Tham75a,
  author =       "Joseph M. Thames",
  title =        "Computing in Calculus",
  journal =      "Research/Development",
  volume =       "",
  number =       "",
  year =         "1975",
  pages =        "24 -- 30",
  referred =     "[Jued91a]; [Tham91a].",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Tham82a,
  author =       "Joseph M. Thames",
  title =        "The Evolution of Synthetic Calculus: {A} Mathematical
                 Technology for Advanced Architecture",
  booktitle =    "Proceedings of the International Workshop on
                 High-Level Language Computer Architecture, University
                 of Maryland",
  publisher =    "",
  year =         "1982",
  pages =        "",
  referred =     "[Jued91a]; [Tham91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Manual{Tham89a,
  author =       "Joseph M. Thames",
  title =        "{FORTRAN} {CALCULUS}: {A} New Implementation of
                 Synthetic Calculus",
  organization = "Digital Calculus Corp.",
  address =      "Torrance, CA 90505",
  year =         "1989",
  referred =     "[Jued91a]; [Tham91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Tham91a,
  author =       "Joseph M. Thames",
  title =        "Synthetic Calculus: {A} Paradigm for Mathematical
                 Program Synthesis",
  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].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Thun84a,
  author =       "M. Thune",
  title =        "A software package for stability analysis of
                 difference methods",
  booktitle =    "{PDE} Software: {Modules}, Interfaces and Systems",
  publisher =    "North-Holland",
  year =         "1984",
  editor =       "B. Engquist and T. Smedsaas",
  pages =        "89",
  referred =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Tomo72a,
  author =       "R. Tomovic and M. Vukobratovic",
  title =        "General Sensitivity Theory",
  publisher =    "Elsevier North-Holland, Inc.",
  series =       "",
  address =      "New York",
  year =         "1972",
  referred =     "[Worl91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Tsuc88a,
  author =       "T. Tsuchiya and Masao Iri",
  title =        "Analysis of rounding errors in large systems of
                 nonlinear equations",
  journal =      "Proceedings of the Institute of Statistical
                 Mathematics",
  volume =       "36",
  number =       "",
  year =         "1988",
  pages =        "1 -- 22",
  note =         "(In Japanese).",
  referred =     "[Irim91a].",
  comment =      "English translation available as {\it RMI 89-02},
                 Department of Mathematical Engineering and
                 Instrumentation Physics, Faculty of Engineering,
                 University of Tokyo, 1989",
  keywords =     "",
  abstract =     "",
}

@Manual{Turn85a,
  author =       "J. R. Turner",
  title =        "Pocket {APL} - Reference Guide",
  organization = "STSC, Inc.",
  address =      "Rockville, MD",
  year =         "1985",
  referred =     "[Garc91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Udwa76a,
  author =       "F. E. Udwadia and Piyush C. Shah",
  title =        "Identification of Structures Through Records Obtained
                 During Strong Earthquake Ground Motion",
  journal =      "Journal of Engineering for Industry",
  volume =       "",
  number =       "",
  month =        nov,
  year =         "1976",
  pages =        "1347 -- 1362",
  referred =     "[Shah91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Ukko81a,
  author =       "E. Ukkonen",
  title =        "On the Calculation of the Effects of Rounding Errors",
  journal =      "ACM Trans. Math. Software",
  volume =       "7",
  number =       "",
  year =         "1981",
  pages =        "259 -- 271",
  referred =     "[Irim91a]; [Kubo91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Manual{UNIC91a,
  author =       "UNICOS",
  title =        "{UNICOS} Performance Utilities Reference Manual,
                 {SR}--2040 6.0",
  organization = "Cray Research, Inc.",
  address =      "",
  year =         "1991",
  referred =     "[Saar91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Urba85a,
  author =       "B. Urban",
  title =        "Maximum Error Growth in Simple Meteorological Models",
  institution =  "Ecole Nationale de la M\'{e}t\'{e}orologie",
  month =        "",
  year =         "1985",
  type =         "Internal report",
  number =       "",
  address =      "Toulouse, France",
  referred =     "[Tala91a].",
  note =         "(In French).",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Veyr90a,
  author =       "P. Veyre",
  title =        "Study of the forecast skill with the {Kalman} filter
                 technique",
  booktitle =    "Proceedings of the International Symposium on
                 Assimilation of Observations in Meteorology and
                 Oceanography, World Meteorological Organization,
                 Geneva, Switzerland",
  publisher =    "",
  year =         "1990",
  pages =        "460",
  referred =     "[Tala91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

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

@Phdthesis{Wang84a,
  author =       "J.-L. Wang",
  title =        "The Computation and Sensitivity Analysis of Economic
                 Equilibrium",
  school =       "Department of Economics, USC",
  year =         "1984",
  address =      "Los Angeles, CA",
  month =        "",
  note =         "",
  referred =     "[Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Wang86a,
  author =       "Paul S. Wang",
  title =        "{FINGER}: {A} symbolic system for automatic
                 generation of numerical programs in finite element
                 analysis",
  journal =      "Journal of Symbolic Computation",
  year =         "1986",
  volume =       "2",
  number =       "3",
  pages =        "305 -- 316",
  month =        sep,
  referred =     "[Char91a].",
  comment =      "Char -- Includes a discussion of code optimization
                 techniques.",
  keywords =     "",
  abstract =     "",
}

@Techreport{Warn75a,
  author =       "D. D. Warner",
  title =        "A partial derivative generator",
  type =         "Computing Science Technical Report",
  number =       "No. 28",
  institution =  "Bell Telephone Laboratories",
  address =      "Murray Hill, NJ 07974",
  year =         "1975",
  referred =     "[Carl86a]; [Hali83a]; [Hill82a]; [Spee80a].",
  comment =      "",
  keywords =     "differentiation arithmetic; precompiler.",
  abstract =     "A precompiler is described which takes a
                 specification of a function as input and produces a
                 Fortran subroutine which will evaluate the component
                 functions and the corresponding Jacobian. Many of the
                 Fortran elementary functions are provided, as well as
                 a facility which allows the user to specify their own
                 differentiation rules.",
}

@Article{Weng64a,
  author =       "R. E. Wengert",
  title =        "A simple automatic derivative evaluation program",
  journal =      "Comm. ACM",
  volume =       "7",
  number =       "8",
  publisher =    "",
  year =         "1964",
  pages =        "463 -- 464",
  referred =     "[Bell65a]; [Carl86a]; [Corl88a]; [Garc91a];
                 [Irim91a]; [Kala83b]; [Laws88a]; [Laws91a]; [Neid87a];
                 [Neid89a]; [Ostr71a]; [Pfei87a]; [Tesf91a]; [Voli85a];
                 [Wexl87a]; [Wilk64a].",
  comment =      "",
  keywords =     "point algorithm; differentiation arithmetic; computer
                 program.",
  abstract =     "A procedure for automatic evaluation of total and
                 partial derivatives of arbitrary algebraic functions
                 is presented. The numerical values of derivatives are
                 computed without developing analytic expressions for
                 the derivatives. The function is decomposed into a
                 sequence of elementary expressions A library is
                 provided for differentiating of elementary functions.",
}

@Phdthesis{Werb74a,
  author =       "Paul Werbos",
  title =        "Beyond Regression: {New} Tools for Prediction and
                 Analysis in the Behavioral Sciences",
  school =       "Committee on Appl. Math., Harvard Univ.",
  address =      "Cambridge, MA",
  month =        nov,
  year =         "1974",
  referred =     "[Saar91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

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

@Article{Werb90a,
  author =       "Paul Werbos",
  title =        "Backpropagation Through Time: What It Does and How To
                 Do It",
  journal =      "Proceedings of the IEEE",
  volume =       "78",
  number =       "10",
  year =         "1990",
  pages =        "1550 -- 1560",
  referred =     "[Saar91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Werb91a,
  author =       "Paul Werbos",
  title =        "Adaptive Networks as Models or Controllers: From
                 Neural Nets to the Genral Case",
  booktitle =    "Proceedings of the Eigth International Conference on
                 Mathematical and Computer Modeling",
  year =         "1991",
  editor =       "Avula",
  publisher =    "Pergamon Press",
  address =      "",
  pages =        "",
  referred =     "[Saar91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Techreport{Wert68a,
  author =       "H. J. Wertz",
  title =        "{SUPER-CODEX}: {Supervisor} plus compiler of
                 differentiable expressions",
  institution =  "Mathematics Research Center, University of
                 Madison-Wisconsin",
  year =         "1972",
  pages =        "",
  referred =     "[Hali83a]; [Rall80a].",
  comment =      "Also Rept. No. TOR--0172(9320)--12, SUPER-CODEX:
                 Analytic differentiation of Fortran statements, The
                 Aerospace Corporation, El Segundo, CA (1972).",
  keywords =     "precompiler.",
  abstract =     "",
}

@Book{Wert88a,
  author =       "J. R. Wertz",
  title =        "Spacecraft Attitude Determination and Control",
  publisher =    "D. Reidel Publishing Co.",
  series =       "",
  address =      "Holland",
  year =         "1988",
  referred =     "[Layn91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Wexl87a,
  author =       "Anthony S. Wexler",
  title =        "Automatic evaluation of derivatives",
  journal =      "Applied Mathematics and Computation",
  volume =       "24",
  number =       "",
  year =         "1987",
  pages =        "19 -- 46",
  referred =     "[Neid89a]; [Tesf91a].",
  comment =      "",
  keywords =     "differentiation arithmetic; computer program.",
  abstract =     "This is an implementation of Wengbert's automatic
                 differentiation method, see [Weng64a], which uses
                 dynamic memory allocation.",
}

@Article{Weis82a,
  author =       "C. R. Weisbing and others",
  title =        "Sensitivity and Uncertainty Analysis of Reactor
                 Performance Parameters",
  journal =      "Advances in Nuclear Science and Technology",
  volume =       "14",
  number =       "",
  month =        "",
  year =         "1982",
  pages =        "",
  referred =     "[Worl91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Wexl88a,
  author =       "Anthony S. Wexler",
  title =        "An Algorithm for Exact Evaluation of Multivariate
                 Functions and Their Derivatives to Any Order",
  journal =      "Computational Statistics and Data Analysis",
  volume =       "6",
  number =       "",
  year =         "1988",
  pages =        "1 -- 6",
  referred =     "[Tesf91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Wilk64a,
  author =       "R. D. Wilkins",
  title =        "Investigation of a new analytic model for numerical
                 derivative evaluation",
  journal =      "Comm. ACM",
  volume =       "7",
  number =       "8",
  publisher =    "",
  year =         "1964",
  pages =        "465 -- 471",
  referred =     "[Bell65a].",
  comment =      "",
  keywords =     "point algorithm; differentiation arithmetic;
                 numerical results.",
  abstract =     "The technique for evaluating derivatives described in
                 [Weng64a] is discussed. The technique is shown to be
                 both easy to use and accurate by use of specific
                 examples.",
}

@Book{Wilk63a,
  author =       "James H. Wilkinson",
  title =        "Rounding Errors in Algebraic Processes",
  publisher =    "Prentice-Hall Inc.",
  series =       "",
  address =      "Englewood Cliffs, NJ",
  year =         "1963",
  referred =     "[Kubo91a].",
  keywords =     "",
  abstract =     "",
}

@Techreport{Wint79a,
  author =       "K. H. Winters and K. A. Cliffe",
  title =        "A finite element study of driven laminar flow in a
                 square cavity",
  institution =  "{AERE} Harwell, Theoretical Physics Division",
  year =         "1979",
  type =         "Technical Report",
  number =       "AERE -- R 9444",
  address =      "",
  month =        "",
  note =         "",
  referred =     "[Bisc91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Phdthesis{Wirtf80a,
  author =       "Michael C. Wirth",
  title =        "On the Automation of Computational Physics",
  school =       "University of California, Davis",
  year =         "1980",
  month =        oct,
  note =         "Also available as Lawrence Livermore National
                 Laboratory, Livermore, Report UCRL-52996 (October
                 1980).",
  referred =     "",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Inproceedings{Wirt81a,
  author =       "Michael C. Wirth",
  title =        "Automatic Generation of Finite Difference Equations
                 and {Fourier} Stability Analysis",
  booktitle =    "{Proceedings of the 1981 ACM Symposium on Symbolic
                 and Algebraic Computation}",
  year =         "1981",
  editor =       "Paul S. Wang",
  pages =        "73 -- 78",
  organization = "{Association of Computing Machinery}",
  referred =     "[Char91a].",
  comment =      "Char -- Automatic generation of finite difference
                 equation.",
  keywords =     "",
  abstract =     "",
}

@Book{Wolf88a,
  author =       "Stephen Wolfram",
  title =        "Mathematica: {A} System for Doing Mathematics by
                 Computer",
  publisher =    "Addison-Wesley",
  series =       "",
  address =      "Reading, MA",
  year =         "1988",
  referred =     "[Gold91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Book{Wolf90a,
  author =       "Stephen Wolfram",
  title =        "Mathematica: {A} System for Doing Mathematics by
                 Computer",
  edition =      "Second",
  publisher =    "Addison-Wesley",
  series =       "",
  address =      "Reading, MA",
  year =         "1990",
  referred =     "[Char91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Woll65a,
  author =       "H. Wollnik",
  title =        "Second order approximation of the three-dimensional
                 trajectories of charged particles in deflecting
                 electrostatic and magnetic fields",
  journal =      "Nuclear Instruments and Methods",
  volume =       "34",
  number =       "",
  month =        "",
  year =         "1965",
  pages =        "213 +",
  referred =     "[Berz91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Woll67a,
  author =       "H. Wollnik",
  title =        "Second order transfer matrices of real magnetic and
                 electrostatic sector fields",
  journal =      "Nuclear Instruments and Methods",
  volume =       "52",
  number =       "",
  month =        "",
  year =         "1965",
  pages =        "250 +",
  referred =     "[Berz91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Woll68a,
  author =       "H. Wollnik",
  title =        "Image aberrations of second order of electrostatic
                 sector fields",
  journal =      "Nuclear Instruments and Methods",
  volume =       "59",
  number =       "",
  month =        "",
  year =         "1965",
  pages =        "277 +",
  referred =     "[Berz91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Woll87a,
  author =       "H. Wollnik",
  title =        "Charged Particle Optics",
  publisher =    "Academic Press",
  series =       "",
  address =      "Orlando, FL",
  year =         "1987",
  referred =     "[Berz91a].",
  comments =     "",
  keywords =     "",
  abstract =     "",
}

@Article{Woll65b,
  author =       "H. Wollnik and H. Ewald",
  title =        "The influence of magnetic and electric fringing
                 fields on the trajectories of charged particles",
  journal =      "Nuclear Instruments and Methods",
  volume =       "36",
  number =       "",
  month =        "",
  year =         "1965",
  pages =        "93 +",
  referred =     "[Berz91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Worl86a,
  author =       "Brian Worley and R. Q. Wright and F. G. Pin and W. V.
                 Harper",
  title =        "Application of an Automated Procedure for Adding a
                 Comprehensive Sensitivity Calculation Capability to
                 the {ORIGEN2} Point Depletion and Radioactivity Decay
                 Code",
  journal =      "Nucl. Sci. Eng.",
  volume =       "94",
  number =       "180",
  year =         "1986",
  pages =        "",
  referred =     "[Horw91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Incollection{Worl91a,
  author =       "Brian Worley",
  title =        "Experience with the Forward and Reverse Mode of
                 {GRESS} in Contaminant Transport Modeling and Other
                 Applications",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  year =         "1991",
  editor =       "Andreas Griewank and George F. Corliss",
  publisher =    "SIAM",
  address =      "Philadelphia, PA",
  pages =        "",
  referred =     "",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Yosh87a,
  author =       "T. Yoshida",
  title =        "Derivation of a Computational Process for Partial
                 Derivatives of Functions Using Transformations of a
                 Graph",
  journal =      "Transactions of IPSJ",
  volume =       "11",
  number =       "",
  year =         "19",
  pages =        "1112 -- 1120",
  referred =     "[Grie91a].",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Article{Yosh89a,
  author =       "T. Yoshida",
  title =        "Automatic derivative derivation system",
  journal =      "Transactions of Information Processing Society of
                 Japan",
  volume =       "30",
  number =       "7",
  year =         "1989",
  pages =        "799 -- 806",
  referred =     "[Jued91a]; [Soul91a].",
  note =         "(In Japanese).",
  comment =      "",
  keywords =     "",
  abstract =     "",
}

@Book{Zack71a,
  author =       "S. Zacks",
  title =        "The Theory of Statistical Inference",
  year =         "1971",
  publisher =    "John Wiley and Sons",
  series =       "",
  address =      "New York",
  referred =     "[Garc91a].",
  keywords =     "",
  abstract =     "",
}