% File: all_brec.bib Updated: 22-NOV-1991, 02-Mar-1994 % % Automatic Differentiation Bibliography, % collected by George F. Corliss, % in Automatic Differentiation of Algorithms: % Theory, Implementation, and Application, % Andreas Griewank and George Corliss (eds.), % SIAM, Philadelphia, PA, 1991. % % This bibliography represents the common bibliography for all of the % papers in this volume. Each author prepared a bibliography for her or % his own paper. The separate bibliographies were merged into a single % BibTex database, and references from several other sources were added. % Especially valuable contributions were made by bibliographic data % bases previously compiled by Bruce Char, by David Gay and by % Davis, Corliss, and Krenz [Davi88a]. % This bibliography includes most of the work known to the editors % in the area of automatic differentiation. Because it includes all of % the works cited by any paper in this volume, it includes many citations % which are not directly related to automatic differentiation. For % example, it includes basic references in optimization, symbolic algebra % systems, and several applications areas. % The electronic form of this bibliography contains many other works % relating to automatic differentiation. The electronic version % is available from netlib (netlib at research.bell-labs.com). Corrections and % additions are welcome and should be sent to % Dr. George F. Corliss, % Department of Mathematics, Statistics, % and Computer Science, % Marquette University, % Milwaukee, WI 53233 USA, % georgec at boris.mscs.mu.edu. % % Assumes commands to get Russian digraphs: % \newcommand{\Yu}{{Yu}} % \newcommand{\Ye}{{Ye}} % \newcommand{\Ju}{{Ju}} @Book{Aber88a, author = "Oliver Aberth", title = "Precise Numerical Analysis", publisher = "William Brown", address = "Dubuque, IA", year = "1988", comment = "Text for a one semester, junior level course in numerical analysis. Includes PC disk with software written in PBASIC. Sound introductory level discussion of code lists and error capture techniques.", keywords = "general numerical analysis; interval techniques; differentiation arithmetic; variable precision arithmetic; linear algebra; differentiation; integration; ordinary differential equations.", abstract = "Aberth addresses elementary issues of precise floating point computations using variable precision range arithmetic. Numbers are represented as a variable precision number $\pm$ a range. Rational arithmetic is also considered. Chapters are devoted to \begin{enumerate} \item rootfinding, \item polynomial rootfinding, \item numerical linear algebra, \item differentiation and integration, and \item ordinary differential equations.\end{enumerate} Differentiation is handled by a codelist approach like [Rall81a], and applications to Taylor series are given. Interval techniques for ordinary differential equations are based on using an {\it a priori\/} bound to capture remainder terms. Several methods are illustrated, including Taylor series methods.", } @Book{Abra70a, editor = "M. Abramowitz and I. A. Stegun", title = "Handbook of Mathematical Functions", publisher = "Dover", series = "", address = "New York", year = "1970", referred = "[Layn91a].", comments = "", keywords = "", abstract = "", } @Inproceedings{Adam69a, author = "D. S. Adamson and C. W. Winant", title = "A {SLANG} Simulation of an Initially Strong Shock Wave Downstream of an Infinite Area Change", booktitle = "Proceedings of the Conference on Applications of Continuous-System Simulation Languages", publisher = "", year = "1969", pages = "231 -- 240", referred = "[Jued91a].", comment = "", keywords = "", abstract = "", } @Manual{AdaLRM, author = "{Ada Joint Program Office}", title = "Reference Manual for the {Ada} Programming Language, {ANSI/MIL--STD--1815A}", organization = "", address = "Washington, DC", year = "1983", referred = "", comment = "", keywords = "", abstract = "", } @Techreport{AFNO83a, author = "AFNOR", title = "Le Langage de Programmation {FORTRAN}", institution = "{Association} {Fran\c{c}aise} de {Normalisation}, {Tour} {Europe}, {Cedex} 7, {F}-92080 {Paris} {La} {D\'{e}fense} {Cedex}", year = "1983", type = "norme {I}{S}{O} 1539 (norme {N}{F} {Z} 65-110)", number = "", address = "", referred = "[Soul91a].", comments = "", keywords = "", abstract = "", } @Book{Ahoa86a, author = "A. V. Aho and R. Sethi and J. D. Ullman", title = "Compilers: {Principles}, Techniques, and Tools", publisher = "Addison-Wesley", series = "", address = "Reading, MA", year = "1986", referred = "[Thac91a].", comments = "", keywords = "", abstract = "", } @Article{Aida89a, author = "K. R. Aida-zade and {\Yu}ri G. Evtushenko", title = "Bystroe avtomaticheskoe differentsirovanie na {{\`{E}}{V}{M}} ({Fast} Automatic Differentiation)", journal = "Matematicheskoe Modelirovanie (Mathematical Modelling)", volume = "1", number = "", year = "1989", pages = "121 -- 139", referred = "[Evtu91a]; [Irim91a].", note = "(In Russian).", comment = "", keywords = "", abstract = "", } @Book{Alfe83a, author = "G. Alefeld and J. Herzberger", title = "Introduction to Interval Computations", publisher = "Academic Press", series = "", address = "New York", year = "1983", referred = "[Irim91a].", comments = "", keywords = "", abstract = "", } @Book{Ande79a, author = "L. Anderson and Nail~H. Ibragimov", title = "Lie-Backlund Transformations in Applications", publisher = "Society for Industrial and Applied Mathematics", series = "SIAM Studies in Applied Mathematics", address = "Philadelphia, PA", year = "1979", referred = "[Mich91a].", comments = "", keywords = "", abstract = "", } @Article{Arbe86a, author = "P. Arbenz and W. Gander", title = "Solving nonlinear eigenvalue problems by algorithmic differentiation", journal = "Computing", volume = "36", year = "1986", pages = "205 -- 215", keywords = "nonlinear eigenvalue problems; differentiation arithmetic; numerical results.", abstract = "The eigenvalues of a matrix $A(\lambda)$ can be found by a zero finding method applied to the determinant function $det(A(\lambda))$. The derivatives of $det(A(\lambda))$ can be found by differentiation arithmetic. The paper presents such an algorithm. Various numerical examples are provided and timing comparisons are given.", } @Book{Arbi87a, author = "M. Arbib", title = "Brains, Machines, and Mathematics", publisher = "Springer Verlag", series = "", address = "Berlin", year = "1987", referred = "[Saar91a].", comments = "", keywords = "", abstract = "", } @Incollection{Ball69a, author = "William E. Ball", title = "{BSOLVE}: {Solution} to a set of nonlinear equations by {Marquardt}'s method", booktitle = "Material and Energy Balance Computations", year = "1969", editor = "Ernest J. Henley and Edward M. Rosen", publisher = "John Wiley and Sons", address = "New York", pages = "560 -- 566", referred = "[Soul91a].", comment = "", keywords = "", abstract = "", } @Incollection{Ball73a, author = "William E. Ball", title = "The {BSOLVE} subroutine", booktitle = "Optimization Techniques with {FORTRAN}", year = "1973", editor = "James L. Kuester and Joe H. Mize", publisher = "McGraw-Hill", address = "New York", pages = "240 -- 250", referred = "[Soul91a].", comment = "", keywords = "", abstract = "", } @Book{Bard74a, author = "Y. Bard", title = "Nonlinear Parameter Estimation", publisher = "Academic Press", series = "", address = "New York", year = "1974", referred = "[Garc91a].", keywords = "", abstract = "", } @Techreport{Bart89a, author = "M. C. Bartholomew-Biggs and Lawrence C. W. Dixon and Z. Maany and M. Mohseninia", title = "Three Papers on Automatic Differentiation Presented at the {IFAC} {Symposium} on ``Dynamic Modelling & Control of National Economies'', July 1989, Edinburgh, Scotland", type = "Technical Report", number = "No. 223", institution = "The Numerical Optimisation Center, Hatfield Polytechnic", address = "Hatfield, UK", year = "1988", pages = "", referred = "", comment = "", note = "Contains Automatic Differentiation of Large Sparse Systems, Automatic Differentiation and Constrained Optimization, and Parallel Automatic Differentiation in Ada Applied to the Navier Stokes Equations.", keywords = "point algorithm; differentiation arithmetic; optimisation.", abstract = "It is shown how the extended operations set of Ada can be used to allow automatic differentiation to be specified in a natural way. This is then applied to solving optimisation problems using the truncated Newton method, see [Dixo86a].", } @Article{Bart80a, author = "David Barton", title = "On Taylor series and stiff equations", journal = "ACM Trans. Math. Software", volume = "6", number = "3", year = "1980", pages = "280 -- 294", referred = "MR 82e 65078; [Corl82a]; [Gupt85a]; [Hali83a].", comment = "", keywords = "point algorithm; Taylor series; stiff; automatic differentiation.", abstract = "Surveys the work of Barton, Willers, and Zahar on Taylor series methods. Gives a predictor-corrector algorithm based on Taylor series. Parts: \begin{enumerate} \item Estimate the local error by matching the series at $ t_r $ and the series at $ t_{r+1} $ at the midpoint. \item Predict stepsize (iteratively) to achieve a fraction of the desired tolerance. This is very expensive. \item The predictor formula is an ordinary Taylor polynomial. The corrector formula uses eigenvalues of the Jacobian to distort the series at $ t_{r+1} $ to compute the actual local contributions of the transients. \item Determine the order of the series. \item Detect when a transient has died away, or when it has reappeared.\end{enumerate} A preprocessor written in PL/1 uses automatic differentiation to write a Fortran program which uses recurrence relations to compute the series.", } @Article{Bart70a, author = "David Barton and I. M. Willers and R. V. M. Zahar", title = "The automatic solution of ordinary differential equations by the method of Taylor series.", journal = "Computer J.", volume = "14", number = "3", year = "1970", pages = "243 -- 248", referred = "[Aber88a]; [Chan74a]; [Chan86a]; [Corl82a]; [Fisc87e]; [Hans80a].", comment = "", keywords = "point algorithms; Taylor series; computer languages; differentiation arithmetic.", abstract = "The paper presents a simple language for the specification of mixed algebraic-ordinary differential systems with initial conditions. The language is specified in a BNF-type form. It is shown how to compile and optimise this language. The authors then apply the automatic differentiation technique of [Moor66a] to generate the Taylor series solution of a system specified in this language. Some simple examples of the language are given, but no numerical results are provided.", } @Incollection{Bart71a, author = "David Barton and I. M. Willers and R. V. M. Zahar", title = "Taylor Series Methods for Ordinary Differential Equations -- {An} Evaluation", booktitle = "Mathematical Software", year = "1971", editor = "John Rice", publisher = "Academic Press", address = "New York", pages = "369--390", referred = "[Fisc87e].", comment = "", keywords = "", abstract = "", } @Article{Baue74a, author = "F. L. Bauer", title = "Computational graphs and rounding errors", journal = "SIAM Journal on Numerical Analysis", volume = "11", number = "", year = "1974", pages = "87 -- 96", referred = "[Char91a]; [Irim91a].", comment = "", keywords = "", abstract = "", } @Article{Baur83a, author = "W. Baur and V. Strassen", title = "The Complexity of Partial Derivatives", journal = "Theoretical Computer Science", volume = "22", year = "1983", pages = "317 -- 330", referred = "[Gold91a]; [Irim91a]; [Kubo91a].", keywords = "", abstract = "", } @Book{Beck88a, author = "Richard A. Becker and John M. Chambers and Allan R. Wilks", title = "The New {S} Language", publisher = "{Wadsworth and Brooks/Cole}", series = "Computer Science Series", address = "Pacific Grove, CA", year = "1988", referred = "[Corl91a].", } @Techreport{Beda59a, author = "L. M. Beda and L. N. Korolev and N. V. Sukkikh and T. S. Frolova", title = "Programs for automatic differentiation for the machine {BESM}", type = "{Technical} {Report}", number = "", institution = "Institute for Precise Mechanics and Computation Techniques, Academy of Science", address = "Moscow, USSR", year = "1959", referred = "[Fisc87e]; [Grie91e]; [Ostr71a].", note = "(In Russian).", comment = "Seems to be the earliest paper on the subject -- Fischer.", keywords = "differentiation arithmetic; computer program.", abstract = "", } @Book{Bell65b, author = "R. E. Bellman and Robert E. Kalaba", title = "Quasilinearization and Nonlinear Boundary Value Problems", publisher = "American Elsevier Publishing Co.", series = "", address = "New York", year = "1965", referred = "[Tham91a].", keywords = "", abstract = "", } @Article{Bell65a, author = "R. E. Bellman and Harriet H. Kagiwada and Robert E. Kalaba", title = "{Wengert}'s Numerical Method for Partial Derivatives, Orbit Determination, and Quasilinearization", journal = "Comm. ACM", year = "1965", volume = "8", number = "4", pages = "231 -- 232", referred = "[Fisc87e]; [Kala83a]; [Tesf91a]", comment = "This is a comment on Wengert's paper, see [Weng64a].", keywords = "point algorithms; partial derivatives.", abstract = "The method presented in [Weng64a] is tested on specific problem. It is shown that the method is valid for this specific problem.", } @Techreport{Berz87a, author = "Martin Berz", title = "The Differential Algebra {FORTRAN} Precompiler {DAFOR}", institution = "Los Alamos National Laboratory", address = "Los Alamos, NM", type = "Technical Report AT--3", number = "TN--87--32", month = "", year = "1987", referred = "[Jued91a].", comment = "", keywords = "", abstract = "", } @Article{Berz87b, author = "Martin Berz", title = "The method of power series tracking for the mathematical description of beam dynamics", journal = "Nuclear Instruments and Methods", volume = "A258", number = "", month = "", year = "1987", pages = "431 +", referred = "[Berz91a]; [Mich91a].", comment = "", keywords = "", abstract = "", } @Article{Berz88a, author = "Martin Berz", title = "{Differential} algebraic description and analysis of trajectories in vacuum electronic devices including spacecharge effects", journal = "IEEE Transactions on Electron Devices", volume = "53", number = "11", month = "", year = "1988", pages = "2002 +", referred = "[Berz91a].", comment = "", keywords = "", abstract = "", } @Article{Berz88b, author = "Martin Berz", title = "Differential Algebraic Treatment of Beam Dynamics to Very High Orders including Applications to Spacecharge", journal = "AIP Conference Proceedings", volume = "177", number = "", year = "1988", pages = "275 +", referred = "[Berz91a].", comment = "", keywords = "", abstract = "", } @Article{Berz89a, author = "Martin Berz", title = "Differential Algebraic Description of Beam Dynamics to Very High Order", journal = "Particle Accelerators", volume = "24", number = "", year = "1989", pages = "109", referred = "[Berz91a]; [Jued91a].", comment = "", keywords = "", abstract = "", } @Incollection{Berz89b, author = "Martin Berz", title = "Differential algebra -- {A} new tool", booktitle = "Proceedings of the 1989 IEEE Particle Accelerator Conference", year = "March 20 -- 23, 1989", editor = "Floyd Bennet and Joyce Kopta", publisher = "IEEE", address = "", pages = "", referred = "[Mich91a].", comment = "IEEE Catalog Number 89CH2669-0", keywords = "", abstract = "", } @Incollection{Berz89c, author = "Martin Berz", title = "The Description of Particle Accelerators using High Order Perturbation Theory on Maps", booktitle = "Physics of Particle Accelerators", volume = "1", year = "1989", editor = "M. Month", publisher = "American Institute of Physics", address = "", pages = "961 +", referred = "[Berz91a].", comment = "", keywords = "", abstract = "", } @Techreport{Berz90a, author = "Martin Berz", title = "Differential Algebra Precompiler Version 3 --- {Reference} Manual", institution = "National Superconducting Cyclotron Laboratory, Michigan State University", type = "Technical Report", number = "MSUCL -- 755", address = "East Lansing, MI 48824", year = "1990", referred = "[Berz91a]; [Jued91a].", comment = "", keywords = "", abstract = "", } @Techreport{Berz90b, author = "Martin Berz", title = "{COSY} {INFINITY} Version 3 Reference Manual", institution = "National Superconducting Cyclotron Lab., Michigan State University", type = "Technical Report", number = "MSUCL -- 751", address = "East Lansing, MI 48824", year = "1990", referred = "[Berz91a]; [Jued91a].", comment = "", keywords = "", abstract = "", } @Article{Berz90c, author = "Martin Berz", title = "Computational Aspects of Design and Simulation: {COSY} {INFINITY}", journal = "Nuclear Instruments and Methods", volume = "A298", number = "", year = "1990", pages = "473 +", referred = "[Berz91a]; [Jued91a].", comment = "", keywords = "", abstract = "", } @Incollection{Berz90d, author = "Martin Berz", title = "{COSY} {INFINITY}, an arbitrary order general purpose optics code", booktitle = "Computer Codes and the Linear Accelerator Community", year = "1990", editor = "", publisher = "Los Alamos LA--11857--C", address = "", pages = "137 +", referred = "[Berz91a]; [Jued91a].", comment = "", keywords = "", abstract = "", } @Article{Berz90e, author = "Martin Berz", title = "Arbitrary order description of arbitrary particle optical systems", journal = "Nuclear Instruments and Methods", volume = "A298", number = "", month = "", year = "1990", pages = "426 +", referred = "[Berz91a].", comment = "", keywords = "", abstract = "", } @Techreport{Berz90f, author = "Martin Berz", title = "The {DA} precompiler {DAFOR}", institution = "Lawrence Berkeley National Laboratory", month = "", year = "1990", type = "{Technical} {Report}", number = "", address = "Berkeley, CA", referred = "[Berz91a].", comment = "", keywords = "", abstract = "", } @Incollection{Berz91a, author = "Martin Berz", title = "Forward Algorithms for High Orders and Many Variables with Application to Beam Physics", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", year = "1991", editor = "Andreas Griewank and George F. Corliss", publisher = "SIAM", address = "Philadelphia, PA", pages = "", referred = "[Flan91a].", comment = "", keywords = "", abstract = "", } @Techreport{Berz91b, author = "Martin Berz", title = "{COSY} {INFINITY} Version 4 Reference Manual", institution = "National Superconducting Cyclotron Lab., Michigan State University", type = "Technical Report", number = "MSUCL -- 771", address = "East Lansing, MI 48824", year = "1991", referred = "[Berz91a].", comment = "", keywords = "", abstract = "", } @Article{Berz91c, author = "Martin Berz", title = "Automatic differentiation as an application of nonarchimedean analysis", journal = "IMACS Annals of Computing and Applied Mathematics", volume = "", number = "", month = "", year = "in print", pages = "", referred = "[Berz91a].", comment = "", keywords = "", abstract = "", } @Article{Berz87c, author = "Martin Berz and H.~Wollnik", title = "The program {HAMILTON} for the analytic solution of the equations of motion in particle optical systems through fifth order", journal = "Nuclear Instruments and Methods", volume = "A258", number = "", month = "", year = "1987", pages = "364 +", referred = "[Berz91a].", comment = "", keywords = "", abstract = "", } @Article{Bigg71a, author = "M. C. Biggs", title = "Minimization algorithms making use of non-quadratic properties of the objective function", journal = "Journal of the Institute of Mathematics and Its Applications", volume = "8", number = "", year = "1971", pages = "315 -- 327", referred = "[Garc91a].", keywords = "", abstract = "", } @Article{Bigg73a, author = "M. C. Biggs", title = "A note on minimization algorithms which make use of non-quadratic properties of the objective function", journal = "Journal of the Institute of Mathematics and Its Applications", volume = "12", number = "", year = "1973", pages = "337 -- 338", referred = "[Garc91a].", keywords = "", abstract = "", } @Incollection{Bisc91a, author = "Christian Bischof", title = "Issues in Parallel Automatic Differentiation", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", year = "1991", editor = "Andreas Griewank and George F. Corliss", publisher = "SIAM", address = "Philadelphia, PA", pages = "", referred = "[Corl91a]; [Layn91a].", comment = "", keywords = "", abstract = "", } @Techreport{Bisc91b, author = "Christian Bischof and Andreas Griewank and David Juedes", title = "Exploiting parallelism in automatic differentiation", institution = "Mathematics and Computer Sciences Division, Argonne National Laboratory", year = "1991", type = "Preprint", number = "MCS--P204--0191", address = "9700 South Cass Ave., Argonne, IL 60439--4801", month = "", note = "To be published in the proceedings of the 1991 ACM International Supercomputing Conference.", referred = "[Bisc91a].", } @Techreport{Bisc91c, author = "Christian Bischof and James Hu", title = "Utilities for Building and Optimizing a Computational Graph for Algorithmic Decomposition", institution = "Mathematics and Computer Sciences Division, Argonne National Laboratory", year = "1991", type = "Technical Memorandum", number = "ANL/MCS--TM--148", address = "9700 South Cass Ave., Argonne, IL 60439--4801", month = apr, note = "", referred = "[Bisc91a].", } @Techreport{Bisc91f, author = "Christian Bischof and Alan Carle and George Corliss and Andreas Griewank and Paul Hovland", title = "Generating Derivative Codes from {Fortran} Programs", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", month = "", year = "1991", type = "Preprint", number = "MCS--P263--0991", address = "9700 S. Cass Ave., Argonne, IL 60439--4801", note = "Also appeared as Technical Report 91185, Center for Research in Parallel Computation, Rice University, Houston, TX 77251.", referred = "[Bisc91g]; [Bisc91h].", comment = "", keywords = "", abstract = "", } @Techreport{Bisc91g, author = "Christian Bischof and Paul Hovland", title = "Using {ADIFOR} to Compute Dense and Sparse {Jacobians}", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", month = oct, year = "1991", type = "Technical Memorandum", number = "ANL/MCS--TM--158", address = "9700 S. Cass Ave., Argonne, IL 60439--4801", referred = "", comment = "", keywords = "", abstract = "", } @Techreport{Bisc91i, author = "Christian Bischof and George Corliss and Andreas Griewank", title = "{ADIFOR} Exception Handling", institution = "Mathematics and Computer Science Division, Argonne National Laboratory", month = "", year = "1991", type = "Technical Memorandum", number = "ANL/MCS--TM--159", address = "9700 S. Cass Ave., Argonne, IL 60439--4801", referred = "", comment = "", keywords = "", abstract = "", } @Book{Bohl87a, author = "G. Bohlender and Ch. Ullrich and J. Wolff von Gudenberg and Louis B. Rall", title = "{Pascal}-{SC}, A Computer Language for Scientific Computation", publisher = "Academic Press", series = "", address = "New York", year = "1987", referred = "[Kubo91a]; [Layn91a].", keywords = "", abstract = "", } @Article{Bord56a, author = "J. L. Bordewijk", title = "Inter-Reciprocity Applied to Electrical Networks", journal = "Applied Science Research, The Netherland, Sect. ~B", volume = "6", number = "", year = "1956", pages = "1 -- 74, ", referred = "[Irim91a].", comment = "", keywords = "", abstract = "", } @Book{Boyl90a, author = "A. Boyle and B. F. Caviness", title = "Future Directions for Research in Symbolic Computing", publisher = "SIAM", series = "", address = "Philadelphia, PA", year = "1990", referred = "[Gold91a].", comments = "", keywords = "", abstract = "", } @Book{Brac68a, author = "J. Bracken and G. P. McCormick", title = "Selected Applications of Nonlinear Programming", publisher = "John Wiley and Sons", series = "", address = "New York", year = "1968", referred = "[Gayd91a].", comments = "", keywords = "", abstract = "", } @Article{Bram61a, author = "J. N. Bramhall", title = "An iterative method for inversion of power series", journal = "Comm. ACM", volume = "4", number = "", year = "1961", pages = "317 -- 318, 503", referred = "[Laws91a].", comment = "", keywords = "", abstract = "", } @Book{Bren73a, author = "Richard P. Brent", title = "Algorithms for Minimization without Derivatives", publisher = "Prentice-Hall", series = "", address = "Englewood Cliffs, NJ", year = "1973", referred = "[Garc91a].", keywords = "", abstract = "", } @Inproceedings{Bren77a, author = "Richard P. Brent and H. T. Kung", title = "Fast algorithms for composition and reversion of multivariate power series", booktitle = "Proceedings of the Conference on Theoretical Computer Science, University of Waterloo, Waterloo, Ontario Canada, August 1977", publisher = "", year = "1977", pages = "149 -- 158", referred = "[Laws91a].", comment = "", keywords = "", abstract = "", } @Article{Bren78a, author = "Richard P. Brent and H. T. Kung", title = "Fast algorithms for manipulating formal power series", journal = "J. ACM", volume = "25", number = "4", year = "1978", pages = "581 -- 595", referred = "[Laws91a].", comment = "", keywords = "", abstract = "", } @Article{Broo83a, author = "B. R. Brooks and R. E. Bruccoleri and B. D. Olafson and D. J. States and S. Swaminathan and M. Karplus", title = "{CHARMM}: {A} Program for Macromolecular Energy, Minimization, and Dynamics Calculations", journal = "J. Computational Chemistry", volume = "4", number = "2", month = "", year = "1983", pages = "187 -- 217", referred = "[Gayd91a].", comment = "", keywords = "", abstract = "", } @Book{Broo88a, author = "A. Brook and D. Kendrick and A. Meerhaus", title = "{GAMS}: {A} User's Guide", publisher = "Scientific Press", series = "", address = "Redwood City, CA", year = "1988", referred = "[Gayd91a].", comments = "", keywords = "", abstract = "", } @Article{Brow64a, author = "K. L. Brown and R. Belbeoch and P. Bounin", title = "First- and second-order magnetic optics matrix equations for the midplane of uniform-field wedge magnets", journal = "Review of Scientific Instruments", volume = "35", number = "", month = "", year = "1964", pages = "481 +", referred = "[Berz91a].", comment = "", keywords = "", abstract = "", } @Techreport{Brow79a, author = "K.~L. Brown", title = "The Ion Optical Program {TRANSPORT}", institution = "SLAC", month = "", year = "1979", type = "Technical Report", number = "No. 91", address = "", referred = "[Berz91a].", comment = "", keywords = "", abstract = "", } @Article{Breu69a, author = "Melvin A. Breuer", title = "Generation of optimal code for expressions via factorization", journal = "Comm. ACM", volume = "12", number = "6", year = "1969", pages = "330 -- 340", referred = "[Char91a]; [Gold91a].", comment = "", keywords = "", abstract = "", } @Article{Byrn87a, author = "George D. Byrne and Alan C. Hindmarsh", title = "Stiff {ODE} Solvers: {A} Review of Current and Coming Attractions", journal = "Journal of Computational Physics", volume = "70", number = "", year = "1987", pages = "1 -- 62", referred = "[Dixo91a].", comment = "", keywords = "", abstract = "", } @Article{Cacu81a, author = "D. G. Cacuci", title = "Sensitivity Theory for Nonlinear Systems. {I}. {Nonlinear} Functional Analysis Approach", journal = "J. Math. Phys.", volume = "22", number = "12", month = "", year = "1981", pages = "2794 -- 2802", referred = "[Bisc91g]; [Worl91a].", comment = "", keywords = "", abstract = "", } @Article{Cacu81b, author = "D. G. Cacuci", title = "Sensitivity Theory for Nonlinear Systems. {II}. {Extension} to Additional Classes of Responses", journal = "J. Math. Phys.", volume = "22", number = "12", month = "", year = "1981", pages = "2803 -- 2812", referred = "[Bisc91g]; [Worl91a].", comment = "", keywords = "", abstract = "", } @Article{Cacu84a, author = "D. G. Cacuci and M. C. G. Hall", title = "Efficient estimation of feedback effects with application to climate models", journal = "J. Atmos. Sci.", volume = "41", number = "", month = "", year = "1984", pages = "2063 -- 2068", referred = "[Tala91a].", comment = "", keywords = "", abstract = "", } @Article{Call88a, author = "D. Callahan and K. Cooper and R. T. Hood and Ken Kennedy and Linda M. Torczon", title = "{ParaScope}: a parallel programming environment", journal = "International Journal of Supercomputer Applications", volume = "2", number = "4", month = dec, year = "1988", pages = "", referred = "", comment = "", keywords = "", abstract = "", } @Book{Care87a, author = "D. C. Carey", title = "The Optics of Charged Particle Beams", publisher = "Harwood", series = "", address = "", year = "1987", referred = "[Berz91a].", comments = "", keywords = "", abstract = "", } @Inproceedings{Carl86a, author = "Bradley R. Carlile", title = "Solution of nonlinear systems of equations on the {FPS} 64-bit family of scientific computers using automatic differentiation", booktitle = "Proceedings of the 1986 array conference (Portland, Oregon)", publisher = "", year = "1986", pages = "142 -- 169", referred = "", comment = "", keywords = "point algorithm; differentiation arithmetic; nonlinear equations; numerical results; computer program.", abstract = "The author considers the solution of nonlinear equations using Newton's method. He presents a method which uses differentiation arithmetic to calculate the Jacobian which is required. This method is compared with a finite differencing approach to calculating the Jacobian on a short pipeline machine, the FPS. The differentiation arithmetic approach outperforms the finite differencing approach on all of the test problems presented solving two of the problems which the finite differencing approach failed to solve.", } @Article{Cart74a, author = "R. D. Carter and L. F. {Kemp, Jr.} and A. C. Pierce and D. L. Williams", title = "Performance Matching with Constraints", journal = "Society of Petroleum Engineers Journal", volume = "", number = "", month = apr, year = "1974", pages = "187 -- 196", referred = "[Shah91a].", comment = "", keywords = "", abstract = "", } @Article{Chan67a, author = "Y. F. Chang", title = "The Conduction-Diffusion Theory of Semiconductor Junctions", journal = "Journal of Applied Physics", volume = "38", number = "2", year = "1967", pages = "534 -- 544", referred = "[Corl91a].", comment = "", keywords = "", abstract = "", } @Incollection{Chan74a, author = "Y. F. Chang", title = "Automatic solution of differential equations", booktitle = "Constructive and Computational Methods for Differential and Integral Equations", series = "Lecture Notes in Mathematics", volume = "430", editor = "D. L. Colton and R. P. Gilbert", publisher = "Springer Verlag", address = "New York", year = "1974", pages = "61 -- 94", referred = "[Chan86a]; [Corl82a]; [Corl88a]; [Hali83a].", comment = "", keywords = "point algorithm; Taylor series; automatic differentiation.", abstract = "Compiler programs ATSCPL and ATSBVP are describes which accept as input up to 99 coupled 4th order differential equations described using simple Fortran statements. The solution program uses the Taylor series method to solve the equations. The paper is a good introduction to the basics of numerical Taylor series methods such as step length control. Various example problems are solved, and results are given.", } @Article{Chan86a, author = "Y. F. Chang", title = "The {ATOMCC} toolbox", journal = "BYTE", volume = "11", number = "4", year = "1986", pages = "215 -- 224", referred = "[Corl88a].", comment = "", keywords = "point algorithm; Taylor series; automatic differentiation.", abstract = "ATOMCC is a pre-processor which accepts a Fortran-like statement of a system of ordinary differential equations and writes a Fortran object program which is run later to solve the system. The object program uses recurrence relations to generate the series and a radius of convergence analysis to choose a stepsize which controls the local error. The program also solves stiff systems. It runs on IBM PC compatible computers up to large mainframes.", } @Misc{Chan91a, author = "Y. F. Chang", title = "A Variable-Order (10 -- $ \infty $) {Taylor} Series Method for Solving {ODE}'s with Integration Steps Almost Equal to the Radii of Convergence", howpublished = "Poster presented at {SIAM} {Workshop} on {Automatic} {Differentiation}, {Breckenridge}, {CO}", month = jan, year = "1991", referred = "[Corl91a].", comments = "", keywords = "", abstract = "", } @Article{Chan82a, author = "Y. F. Chang and George F. Corliss", title = "Solving Ordinary Differential Equations Using {Taylor} Series", journal = "ACM Trans. Math. Software", volume = "8", number = "2", year = "1982", pages = "114 -- 144", referred = "[Corl91a]; [Jued91a].", comment = "", keywords = "", abstract = "", } @Article{Chan81a, author = "Y. F. Chang and Mike Tabor and John Weiss and George F. Corliss", title = "On the Analytic Structure of the {Henon}-{Heiles} System", journal = "Physics Letters", volume = "85A", number = "4", year = "1981", pages = "211 -- 213", referred = "[Corl91a].", comment = "", keywords = "", abstract = "", } @Incollection{Char91a, author = "Bruce W. Char", title = "Computer Algebra as a Toolbox for Program Generation and Manipulation", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", year = "1991", editor = "Andreas Griewank and George F. Corliss", publisher = "SIAM", address = "Philadelphia, PA", pages = "", referred = "[Garc91a]; [Gold91a]; [Irim91a].", comment = "", keywords = "", abstract = "", } @Article{Char86a, author = "Bruce W. Char and G. J. Fee and Keith O. Geddes and Gaston H. Gonnet and Michael B. Monagan", title = "A Tutorial Introduction to {MAPLE}", journal = "Journal of Symbolic Computation", volume = "2", number = "2", year = "1986", pages = "179 -- 200", referred = "[Char91a]; [Gold91a].", comment = "", keywords = "", abstract = "", } @Book{Char88a, author = "Bruce W. Char and Keith O. Geddes and Gaston H. Gonnet and Michael B. Monagan and Stephen M. Watt", title = "{MAPLE} Reference Manual", publisher = "Watcom Publications", address = "Waterloo, Ontario Canada", year = "1988", referred = "[Corl91a]; [Gold91a].", comment = "", keywords = "", abstract = "", } @Article{Chav75a, author = "G. Chavent and M. Dupuy and P. Lemmonier", title = "History Matching by Use of Optimal Theory", journal = "Society of Petroleum Engineers Journal", volume = "", number = "", month = feb, year = "1975", pages = "74 -- 86", referred = "[Shah91a].", comment = "", keywords = "", abstract = "", } @Inproceedings{Chao90a, author = "W. C. Chao and L. P. Chang", title = "Status of the development of a variational data assimilation system using the adjoint method at {Goddard} {Laboratory} for {Atmospheres}", booktitle = "Proceedings of the International Symposium on Assimilation of Observations in Meteorology and Oceanography, World Meteorological Organization, Geneva, Switzerland", publisher = "", year = "1990", pages = "355 -- 358", referred = "[Tala91a].", comment = "", keywords = "", abstract = "", } @Article{Chen74a, author = "W. H. Chen and G. R. Gavalas and J. H. Seinfeld and M. L. Wasserman", title = "A New Algorithm for Automatic History Matching", journal = "Society of Petroleum Engineers Journal", volume = "", number = "", month = dec, year = "1974", pages = "593 -- 608", referred = "[Shah91a].", comment = "", keywords = "", abstract = "", } @Techreport{Chri90a, author = "Bruce D. Christianson", title = "Automatic {Hessians} by reverse accumulation", type = "Technical Report", number = "NOC TR228", institution = "The Numerical Optimisation Center, Hatfield Polytechnic", address = "Hatfield, UK", month = apr, year = "1990", referred = "[Bisc91a]; [Dixo91a]; [Jued91a].", comment = "", keywords = "", abstract = "", } @Misc{Chri91a, author = "Bruce Christianson", title = "Automatic {Hessians} by Reverse Accumulation in {Ada}", howpublished = "Poster presented at {SIAM} {Workshop} on {Automatic} {Differentiation}, {Breckenridge}, {CO}. Submitted to {\sl {IMA} {Journal} of {Numerical} {Analysis}\/}", month = jan, year = "1991", referred = "[Corl91a].", comments = "", keywords = "", abstract = "", } @Article{Civa65a, author = "P. P. Civalleri", title = "Cohn's Generalized Theorem", journal = "Alta Frequenza", year = "1965", volume = "35", number = "", pages = "797 -- 806", month = "", note = "", referred = "[Irim91a]", comment = "", keywords = "", abstract = "", } @Book{Clar83a, author = "Frank H. Clark", title = "Optimization and Nonsmooth Analysis", publisher = "John Wiley and Sons", series = "", address = "New York", year = "1983", referred = "", keywords = "", abstract = "", } @Article{Cole84a, author = "T. F. Coleman and B. S. Garbow and J. J. Mor\'{e}", title = "Software for estimating sparse {Jacobian} matrices", journal = "ACM Trans. Math. Software", year = "1984", volume = "10", number = "", pages = "329 -- 345", month = "", note = "", referred = "[Bisc91a].", comment = "", keywords = "", abstract = "", } @Article{Cole83a, author = "T. F. Coleman and J. J. Mor\'{e}", title = "Estimation of sparse {Jacobian} matrices and graph coloring problems", journal = "SIAM Journal on Numerical Analysis", year = "1984", volume = "20", number = "", pages = "187 -- 209", month = "", note = "", referred = "[Bisc91a]; [Grie91a].", comment = "Griewank gives pages as 368 -- 375.", keywords = "", abstract = "", } @Book{Cont80a, author = "S.~D. Conte and Carl {de~Boor}", title = "Elementary Numerical Analysis", publisher = "McGraw-Hill", series = "", address = "New York", year = "1980", referred = "[Berz91a].", comments = "", keywords = "", abstract = "", } @Techreport{Cook88a, author = "Grant O. {Cook, Jr.}", title = "{ALPAL}, a Tool for the Development of Large-scale Simulation Codes", institution = "Lawrence Livermore National Laboratory", type = "Technical Report", address = " Berkley, CA", month = aug, year = "1988", number = "UCID-21482", referred = "[Char91a].", comments = "", keywords = "", abstract = "", } @Incollection{Corl87b, author = "George F. Corliss", title = "Performance of self-validating quadrature", booktitle = "Proceedings of the NATO Advanced Workshop on Numerical Integration: Recent Developments, Software, and Applications", editor = "Pat Keast and Graeme Fairweather", publisher = "Reidel", address = "Boston", year = "1987", pages = "239 -- 259", referred = "Zbl. Math 615 -- 65018; [Corl88a]; [Corl91a].", comment = "quadrature for integral iteration.", keywords = "interval quadrature; automatic differentiation.", abstract = "The interval implementation of Gaussian quadrature described in [Corl87a] required about 3 - 5 times as long to compute a guaranteed bound the $ \int_a^b f(x)\,dx $ as QUADPACK required to compute an estimate.", } @Incollection{Corl88a, author = "George F. Corliss", title = "Applications of Differentiation Arithmetic", booktitle = "Reliability in Computing", publisher = "Academic Press", editor = "Ramon E. Moore", address = "London", year = "1988", pages = "127 -- 148", referred = "[Layn91a].", comment = "Summary of the work performed by the author in the field of differentiation arithmetic.", keywords = "point algorithms; interval algorithms; differentiation arithmetic; preprocessor; quadrature; Taylor series.", abstract = "This is a discussion of various issues involved in differentiation arithmetic. The use in both point and interval algorithms is discussed. Differentiation arithmetic is implemented using the recursion relations for Taylor coefficients, or by using a parser to create a Fortran subroutine which evaluates the derivatives using differentiation arithmetic. Applications to quadrature and to Taylor series solutions of ordinary differential equations is discussed.", } @Incollection{Corl91a, author = "George F. Corliss", title = "Overloading Point and Interval {Taylor} Operators", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", year = "1991", editor = "Andreas Griewank and George F. Corliss", publisher = "SIAM", address = "Philadelphia, PA", pages = "", referred = "[Jued91a]; [Kalm91a]; [Layn91a].", comment = "", keywords = "", abstract = "", } @Article{Corl82a, author = "George F. Corliss and Y. F. Chang", title = "Solving Ordinary Differential Equations Using {Taylor} Series", journal = "ACM Trans. Math. Software", volume = "8", number = "2", publisher = "", year = "1982", pages = "114 -- 144", referred = "MR 83g 65072; [Aber88a]; [Chan86a]; [Corl88a]; [Gupt85a].", comment = "", keywords = "point algorithm; Taylor series; radius of convergence; pre-processing; automatic differentiation.", abstract = "A Fortran pre-processor program uses automatic differentiation to write a Fortran object program which is then run to solve the system. Parts: \begin{enumerate} \item Expand the series using recurrence relations. \item Estimate the radius of convergence of each component. \item Select a step size by comparison with series for model problems. \item Extend the solution by analytic continuation.\end{enumerate} The series analysis provides valuable information about analytic properties of the solution like the location and order of primary singularities. Taylor series methods are shown to be competitive with DVERK and DGEAR in terms of speed and accuracy.", } @Techreport{Corl88b, author = "George F. Corliss and Paul H. Davis and Gary S. Krenz", title = "Bibliography on Interval Methods for the Solution of Ordinary Differential Equations", type = "Technical Report", number = "No. 289", institution = "Department of Mathematics, Statistics and Computer Science, Marquette University", address = "Milwaukee, WI 53233", month = sep, year = "1988", referred = "[Davi88b].", comment = "Contains some intersection with this report. Extension of [Corl87c].", keywords = "bibliography.", abstract = "This is a bibliography of literature judged by the authors to be relevant to interval methods for the numerical solution of initial value problems in ordinary differential equations. It includes citations from the following topics: \begin{itemize} \item Interval methods for initial value problems, \item Interval methods for boundary value problems, \item Point Taylor series methods, \item Point defect correction methods, \item Point methods based on Picard iteration, \item Error {\em estimation\/} for stiff equations, \item Global error {\em estimation,} \item Differentiation arithmetic, and \item Interval integration.\end{itemize}", } @Misc{Corl91c, author = "Robert M. Corless and George F. Corliss", title = "Automatic Differentiation in Validated Defect Control for Ordinary Differential Equations", howpublished = "Poster presented at {SIAM} {Workshop} on {Automatic} {Differentiation}, {Breckenridge}, {CO}. Submitted to {\sl {IMA} {Journal} of {Numerical} {Analysis}\/}", month = jan, year = "1991", referred = "", comment = "", keywords = "", abstract = "", } @Article{Corl87a, author = "George F. Corliss and Louis B. Rall", title = "Adaptive, Self-Validating Quadrature", journal = "SIAM J. Sci. Stat. Comput.", volume = "8", number = "5", year = "1987", pages = "831 -- 847", referred = "[Garl85a] \# 311; [Garl87a] \# 311; [Corl88a]; [Jued91a]; [Rall91a].", comment = "Also {\sl MRC Technical Summary Report No. 2815,\/} University of Wisconsin-Madison, 1985.", keywords = "quadrature; automatic differentiation.", abstract = "Validated bounds for $ If = \int_a^b f(x)\,dx $ are computed using Gaussian, Newton-Cotes, or Taylor polynomial quadrature. The algorithm uses both subinterval and order adaptation. Results often differ by a few units in the last place.", } @Incollection{Corl84a, author = "George F. Corliss and Louis B. Rall", title = "Automatic generation of {Taylor} series in {Pascal}-{SC}: {Basic} operations and applications to differential equations", booktitle = "Trans. of the First Army Conference on Applied Mathematics and Computing (Washington, DC, 1983)", publisher = "ARO Rep. 84-1, U. S. Army Res. Office", address = "Research Triangle Park, NC", year = "1984", pages = "177 -- 209", referred = "CMP 741 340; [Garl85a] \# 310; [Garl87a] \# 310; [Corl88a]; [Fisc87e]; [Jued91a]; [Rall87a].", comment = "Also appeared as {\sl MRC Technical Summary Report No.2497,\/} Mathematics Research Center, University of Wisconsin-Madison, 1983.", keywords = "automatic differentiation; Taylor series; stability.", abstract = "Pascal-SC supports user-defined data types, user-defined operators, and accurate floating point and interval arithmetic for numerical computations. The authors implement data types TAYLOR and ITAYLOR (Interval Taylor) with operators $ + $, $ - $, $ * $, $ / $, $ ** $, and the functions SQR, SQRT, EXP, SIN, COS, ARCTAN, and LN. An initial value problem $ y' = y^2 $, $ y(0) = 1 $, is solved with TAYLOR and with ITAYLOR types to show that the series generation exhibits a mild instability which has no significant effect on the values of the solution computed by analytic continuation.", } @Incollection{Corl91b, author = "George F. Corliss and Louis B. Rall", title = "Computing the Range of Derivatives", booktitle = "{IMACS} Annals on Computing and Applied Mathematics", year = "to appear", pages = "", publisher = "{IMACS}", address = "", series = "{IMACS} Annals on Computing and Applied Mathematics", note = "", referred = "[Corl91a]; [Jued91a]; [Rall91a].", comment = "", keywords = "", abstract = "", } @Inproceedings{Cour85a, author = "P. Courtier", title = "Experiments in Data Assimilation Using the Adjoint Model Technique", booktitle = "Proceedings of the Workshop on High-Resolution Analysis ECMWF (UK)", publisher = "", month = jun, year = "1985", pages = "", referred = "[Navo91a].", comment = "", keywords = "", abstract = "", } @Techreport{Cour87b, author = "P. Courtier", title = "Application of Optimal Control to Numerical Meteorological Forecasting", type = "{Doctoral} thesis", institution = "Universit\'{e} Pierre-et-Marie-Curie", address = "Paris, France", month = "", year = "1987", referred = "[Tala91a].", note = "(In French).", comment = "", keywords = "", abstract = "", } @Article{Cour87a, author = "P. Courtier and Olivier Talagrand", title = "Variational Assimilation of Meteorological Observations with the Adjoint Equation -- {Part} {II}. {Numerical} Results", journal = "Q. J. R. Meteorol. Soc.", volume = "113", number = "", month = "", year = "1987", pages = "1329 -- 1347", referred = "[Navo91a].", comment = "", keywords = "", abstract = "", } @Article{Cour90a, author = "P. Courtier and Olivier Talagrand", title = "Variational Assimilation of Meteorological Observations with the Direct and Adjoint Shallow-Water Equations", journal = "Tellus", volume = "42A", number = "", month = "", year = "1990", pages = "531 -- 549", referred = "[Tala91a].", comment = "", keywords = "", abstract = "", } @Inproceedings{Cour90b, author = "P. Courtier and J. N. Thepaut and Olivier Talagrand", title = "4-dimensional data assimilation using the adjoint of a primitive equation model", booktitle = "Proceedings of the International Symposium on Assimilation of Observations in Meteorology and Oceanography, World Meteorological Organization, Geneva, Switzerland", publisher = "", year = "1990", pages = "337 -- 340", referred = "[Tala91a].", comment = "", keywords = "", abstract = "", } @Techreport{Crar75a, author = "F. D. Crary", title = "The {AUGMENT} precompiler. {II}. Technical documentation", type = "MRC Technical Summary Report", number = "No. 1470", institution = "Mathematics Research Center, University of Madison-Wisconsin", year = "1975", referred = "[Corl91a]; [Crar79a]; [Rall80a].", comment = "AUGMENT is important as a possible vehicle for the implementation of differentiation arithmetic and/or interval arithmetic.", keywords = "precompiler.", abstract = "", } @Techreport{Crar76a, author = "F. D. Crary", title = "The {AUGMENT} precompiler. I. User information", type = "MRC Technical Summary Report", number = "No. 1469", institution = "Mathematics Research Center, University of Madison-Wisconsin", year = "1976", pages = "", referred = "[Crar79a]; [Rall80a].", comment = "AUGMENT is important as a possible vehicle for the implementation of differentiation arithmetic and/or interval arithmetic.", keywords = "precompiler.", abstract = "", } @Article{Crar79a, author = "F. D. Crary", title = "A versatile precompiler for nonstandard arithmetics", journal = "ACM Trans. Math. Software", year = "1979", volume = "5", number = "2", pages = "204 -- 217", referred = "[Corl87a]; [Corl88a]; [Yohe79a].", comment = "", keywords = "precompiler; nonstandard arithmetics.", abstract = "A highly portable Fortran precompiler which allows simplified computation with nonstandard arithmetics is described. The philosophy and design goals are briefly presented, the major capabilities of the precompiler are described, and some applications are discussed. A summary is made of experience with the precompiler. The author's aim is to furnish programmers with a ready means of using nonstandard arithmetics.", } @Article{Datt91a, author = "S. Datta and J. Nugent and A. Tishler and J. L. Wang", title = "Seasonality, Differential Access, and Interlinking of Labour and Credit", journal = "Journal of Development Studies", year = "to appear", volume = "", number = "", pages = "", referred = "[Tesf91a]", } @Book{Davi81a, author = "A. J. T. Davie and R. Morrison", title = "Recursive Descent Compiling", publisher = "Ellis-Horwood", series = "", address = "Chichester", year = "1981", referred = "[Garc91a].", keywords = "", abstract = "", } @Techreport{Davi88a, author = "Paul H. Davis and George F. Corliss and Gary S. Krenz", title = "A Bibliography on Methods and Techniques in Differentiation Arithmetic", type = "Technical Report", number = "{AM}--88--09", institution = "Maths. Dept., Bristol University", address = "Bristol, UK", year = "1988", referred = "[Corl91a]; [Davi88b].", comment = "Basis for this bibliography.", keywords = "differentiation arithmetic, bibliography.", abstract = "The authors gather together all references known to them relating to methods, techniques, algorithms, or applications of differentiation arithmetic.", } @Techreport{Davi87a, author = "Paul H. Davis and John D. Pryce", title = "A New Implementation of Automatic Differentiation for Use with Numerical Software", type = "Technical Report", number = "AM--87--11", institution = "School of Mathematics, University of Bristol", address = "Bristol, UK", year = "1987", pages = "", referred = "[Step87a].", comment = "", keywords = "point algorithm; differentiation arithmetic; parser.", abstract = "A sparse automatic differentiation technique for calculating partial derivatives is presented. The algorithms only calculate the derivatives of a function which are not identically zero. The algorithms derived can be used to calculate the derivatives of a function to an arbitrary level. It is shown how to implement the technique in a numerical software package using a parsing technique.", } @Techreport{Davi88b, author = "Paul H. Davis and Bruce Stephens and George F. Corliss and Gary S. Krenz", title = "Specification of a Preprocessor for Use with Differentiation Arithmetic", type = "Technical Report", number = "AM--88--08", institution = "School of Mathematics, University of Bristol", address = "Bristol, UK", year = "1988", month = sep, referred = "", comment = "", keywords = "differentiation arithmetic, coder.", abstract = "This report documents discussions held by the authors on the specification and design of a general purpose computer package to support differentiation arithmetic. They consider the rationale and applications of differentiation arithmetic, outline the general structure of a coder-operators system, and describe the specifications for the coder, the operators, and their interface.", } @Article{Denn81a, author = "John Dennis and David Gay and R. E. Welsch", title = "Algorithm 573. {NL2SOL} --- {An} Adaptive Nonlinear Least-Squares Algorithm", journal = "ACM Trans. Math. Software", volume = "7", number = "", month = "", year = "1981", pages = "369 -- 383", referred = "[Gayd91a].", comment = "", keywords = "", abstract = "", } @Book{Denn83a, author = "John Dennis and R. Schnabel", title = "Numerical Methods for Unconstrained Optimization and Nonlinear Equations", publisher = "Prentice-Hall", year = "1983", volume = "", series = "", address = "Englewood Cliffs, NJ", edition = "", month = "", referred = "[Bisc91a].", comment = "", keywords = "", abstract = "", } @Phdthesis{Derb85a, author = "J. C. Derber", title = "The Variational 4-D Assimilation of Analyses Using Filtered Models as Constraints", school = "University of Wisconsin-Madison", address = "Madison, WI", month = "", year = "1985", referred = "[Navo91a].", comment = "", keywords = "", abstract = "", } @Inproceedings{Dewa89a, author = "M. C. Dewar", title = "{IRENA} --- {An} integrated symbolic and numerical computational environment", booktitle = "Proceedings of the 1989 International Symposium on Symbolic and Algebraic Computation", year = "1989", editor = "Gaston H. Gonnet", pages = "171 -- 179", referred = "[Char91a].", comment = "", keywords = "", abstract = "", } @Inproceedings{Dewa90a, author = "M. C. Dewar and M. G. Richardson", title = "Reconciling Symbolic and Numeric Computation in a Practical Setting", booktitle = "Design and Implementation of Symbolic Computing Systems, Proceedings of DISCO 90", year = "1990", editor = "A. Miola", pages = "195 -- 204", publisher = "Springer Verlag", address = "Berlin", month = apr, series = "Lecture Notes in Computer Science, No. 429.", note = "", referred = "[Char91a].", comment = "", keywords = "", abstract = "", } @Techreport{LeDi82a, author = "F.-X. {Le Dimet}", title = "A General Formalism of Variational Analysis", institution = "IMMS", month = "", year = "1982", type = "Report", number = "No. 22", address = "Norman, OK 73091", referred = "[Navo91a].", comment = "", keywords = "", abstract = "", } @Incollection{LeDi86b, author = "F.-X. {Le Dimet} and A. Nouailler", title = "Assimilation of Dynamic Data in a Limited-Area Model", booktitle = "Variational Methods in Geosciences", year = "1986", editor = "Y. K. Sasaki", publisher = "Elsevier", address = "Amsterdam", pages = "181 -- 198", referred = "[Navo91a].", comment = "", keywords = "", abstract = "", } @Article{LeDi86a, author = "F.-X. {Le Dimet} and O. Talagrand", title = "Variational algorithms for analysis and assimilation of meteorological observations: {Theoretical} aspects", journal = "Tellus", volume = "38A", number = "", year = "1986", pages = "97 -- 110", referred = "[Thac91a].", comment = "", keywords = "", abstract = "", } @Techreport{Dixo87a, author = "Lawrence C. W. Dixon", title = "Automatic Differentiation and Parallel Processing in Optimisation", type = "Technical Report", number = "No. 180", institution = "The Numerical Optimisation Center, Hatfield Polytechnic", address = "Hatfield, UK", year = "1987", referred = "[Bisc91a].", comment = "", keywords = "point algorithm; numerical results; differentiation arithmetic. optimisation method.", abstract = "The concepts of automatic differentiation, see [Rall81a], and of parallel processing are applied to problems in optimisation. A discussion is presented of how the advent of the Ada programming language on parallel processing machines may transform the solution of practical optimisation problems, see [Dixo87b]. The author also discusses the difficulties associated with calculating the derivative values if automatic differentiation is not used.", } @Incollection{Dixo91a, author = "Lawrence C. W. Dixon", title = "Use of Automatic Differentiation for Calculating {Hessians} and {Newton} Steps", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", year = "1991", editor = "Andreas Griewank and George F. Corliss", publisher = "SIAM", address = "Philadelphia, PA", pages = "", referred = "[Grie91a].", comment = "", keywords = "", abstract = "", } @Techreport{Dixo87b, author = "Lawrence C. W. Dixon and M. Mohseninia", title = "The Use of the Extended Operations Set of {ADA} with Automatic Differentiation and the Truncated {Newton} Method", type = "Technical Report", number = "No. 176", institution = "The Numerical Optimisation Center, Hatfield Polytechnic", address = "Hatfield, UK", year = "1987", pages = "", referred = "[Dixo87a]; [Dixo89b]; [Pric87a].", comment = "", keywords = "point algorithm; differentiation arithmetic; optimisation.", abstract = "It is shown how the extended operations set of Ada can be used to allow automatic differentiation to be specified in a natural way. This is then applied to solving optimisation problems using the truncated Newton method, see [Dixo86a].", } @Techreport{Dixo87c, author = "Lawrence C. W. Dixon and Z. Maany", title = "The Echelon Method for the Solution of Sparse Sets of Linear Equations", type = "Technical Report", number = "NOC TR177", institution = "The Numerical Optimisation Center, Hatfield Polytechnic", address = "Hatfield, UK", month = feb, year = "1988", pages = "", referred = "[Dixo91a].", comment = "", keywords = "", abstract = "", } @Techreport{Dixo89b, author = "Lawrence C. W. Dixon and Z. Maany", title = "The Performance of the Truncated Newton, Conjugate Gradient Algorithm in {Fortran} and {Ada}", type = "Technical Report", number = "NOC TR210", institution = "The Numerical Optimisation Center, Hatfield Polytechnic", address = "Hatfield, UK", month = jun, year = "1989", pages = "", referred = "", comment = "", keywords = "optimization", abstract = "We compare the performance of Fortran and Ada implementations of the truncated Newton, conjugate gradient approach for solving unconstrained optimization problems. Automatic differentiation is used to calculate first and second derivatives in both Fortran and Ada -- Authors' abstract.", } @Techreport{Dixo88b, author = "Lawrence C. W. Dixon and Z. Maany and M. Mohseninia", title = "Finite Element Optimization in {ADA} Using Automatic Differentiation", type = "Technical Report", number = "NOC TR205", institution = "The Numerical Optimisation Center, Hatfield Polytechnic", address = "Hatfield, UK", month = "", year = "1988", pages = "", referred = "", comment = "", keywords = "point algorithm; differentiation arithmetic; optimisation.", abstract = "It is shown how the extended operations set of Ada can be used to allow automatic differentiation to be specified in a natural way. This is then applied to solving optimisation problems using the truncated Newton method, see [Dixo86a].", } @Article{Dixo90a, author = "Lawrence C. W. Dixon and Z. Maany and M. Mohseninia", title = "Automatic Differentiation of Large Sparse Systems", journal = "Journal of Economic Dynamics \& Control", volume = "14", number = "2", year = "1990", pages = "", referred = "[Dixo91a].", note = "Presented at IFAC on Dynamic Modelling \& Control of National Economies, Edinburgh, July, 1989. Also appeared as Technical Report NOC TR223, The Numerical Optimisation Center, Hatfield Polytechnic, Hatfield, UK, July, 1989.", comment = "", keywords = "", abstract = "", } @Techreport{Dixo87d, author = "Lawrence C. W. Dixon and M. Mohseninia", title = "The Use of the Extended Operations Set of {Ada} with Automatic Differentiation and the Truncated {Newton} Method", type = "Technical Report", number = "NOC TR176", institution = "The Numerical Optimisation Center, Hatfield Polytechnic", address = "Hatfield, UK", month = apr, year = "1987", referred = "[Dixo91a].", comment = "", keywords = "", abstract = "", } @Techreport{Dixo86a, author = "Lawrence C. W. Dixon and Richard C. Price", title = "The Truncated {Gauss}-{Newton} Method for Sparse Least Squares Problems Using Automatic Differentiation", type = "Technical Report", number = "No. 171", institution = "The Numerical Optimisation Center, Hatfield Polytechnic", address = "Hatfield, UK", year = "1986", referred = "[Dixo87a]; [Fisc87e].", comment = "", keywords = "point algorithm; numerical results; differentiation arithmetic; optimisation method.", abstract = "The automatic differentiation technique described in [Dixo86a] is applied to the solution of least squares problems using a truncated Gauss-Newton method. The method is tested on eight standard test problems.", } @Techreport{Dixo86c, author = "Lawrence C. W. Dixon and P. Dolan and Richard C. Price", title = "Finite Element Optimisation: {The} Use of Structured Automatic Differentiation", type = "Technical Report", number = "No. 175", institution = "The Numerical Optimisation Center, Hatfield Polytechnic", address = "Hatfield, UK", year = "1986", referred = "[Fisc87e].", comment = "", keywords = "point algorithm; numerical results; differentiation arithmetic; optimisation method.", abstract = "A finite element optimisation algorithm is presented which uses the technique of automatic differentiation described in [Dixo86a]. The method is illustrated by reference to two dimensional flow problems that have been implemented on the ICL (AMT) DAP parallel processing computer.", } @Techreport{Dixo86b, author = "Lawrence C. W. Dixon and Richard C. Price", title = "The Truncated {Newton} Method for Sparse Unconstrained Optimisation Using Automatic Differentiation", type = "Technical Report", number = "NOC TR170", institution = "The Numerical Optimisation Center, Hatfield Polytechnic", address = "Hatfield, UK", month = oct, year = "1986", pages = "", referred = "[Dixo87a]; [Dixo91a]; [Fisc87e].", comment = "This paper was presented at the SIAM National meeting, Boston, 1986. Also to appear in J. Opt. Theory and Appl. 60(2), pp. 261 -- 275, February 1989.", keywords = "point algorithm; numerical results; differentiation arithmetic; optimisation method.", abstract = "A method is presented which solves unconstrained optimisation problems using a truncated Newton method. Automatic differentiation is used to calculate the derivatives required. By taking advantage of the structure of the optimisation method, only vector storage is required since the Hessian is multiplied by a vector during the computation of the derivatives. Numerical results obtained by solving standard test problems are presented.", } @Article{Dixo89a, author = "Lawrence C. W. Dixon and Richard C. Price", title = "The Truncated {Newton} Method for Sparse Unconstrained Optimisation Using Automatic Differentiation", journal = "J. Opt. Theory and Appl.", volume = "60", number = "2", month = feb, year = "1989", pages = "261 +", referred = "[Dixo91a].", comment = "", keywords = "point algorithm; numerical results; differentiation arithmetic; optimisation method.", abstract = "A method is presented which solves unconstrained optimisation problems using a truncated Newton method. Automatic differentiation is used to calculate the derivatives required. By taking advantage of the structure of the optimisation method, only vector storage is required since the Hessian is multiplied by a vector during the computation of the derivatives. Numerical results obtained by solving standard test problems are presented.", } @Article{Dixo88a, author = "L. C. W. Dixon and Richard C. Price", title = "Numerical experience with the truncated {Newton} method", journal = "J. Opt. Theory and Appl.", volume = "56", number = "2", year = "1988", pages = "245 -- 255", referred = "[Dixo87a].", comment = "Also appeared in {\sl Technical Report No. 169\/,} The Numerical Optimisation Center, Hatfield Polytechnic, Hatfield, UK (1986).", keywords = "point algorithm; numerical results; optimisation method.", abstract = "The truncated Newton method is presented for use with large sparse unconstrained optimisation problems. It is tested on four problems under various conditions.", } @Article{Drey69a, author = "S. E. Dreyfus", title = "An appraisal of some shortest path algorithms", journal = "Operations Research", volume = "17", number = "", year = "1969", pages = "395 -- 412", referred = "[Irim91a].", comment = "", keywords = "", abstract = "", } @Incollection{Dole90a, author = "Y. Doleh and P. S. Wang", title = "{SUI}: {A} system independent user interface for an integrated scientific computing environment", booktitle = "Proceedings ISSAC '90", year = "1990", editor = "S. Watanabe and M. Nagata", publisher = "ACM-Press", address = "New York", pages = "88 -- 95", referred = "[Gold91a].", comment = "", keywords = "", abstract = "", } @Inproceedings{Doua90a, author = "D. Douady and Olivier Talagrand", title = "The impact of threshold processes on variational assimilation", booktitle = "Proceedings of the International Symposium on Assimilation of Observations in Meteorology and Oceanography, World Meteorological Organization, Geneva, Switzerland", publisher = "", year = "1990", pages = "486 -- 487", referred = "[Tala91a].", comment = "", keywords = "", abstract = "", } @Techreport{Duff87a, author = "I. S. Duff and M. Anoli and N. I. M. Gould and J. K. Reid", title = "The Practical Use of the {Hellerman}-{Ranck} P$^4$ Algorithm and the P$^5$ Algorithm of {Erisman} et al.", institution = "AERE Harwell", month = "", year = "1987", type = "Report", number = "CSS213", address = "", referred = "[Dixo91a].", comment = "", keywords = "", abstract = "", } @Book{Duff86a, author = "I. S. Duff and A. M. Erisman and J. K. Reid", title = "Direct Methods for Sparse Matrices", publisher = "Clarendon Press", series = "Oxford Science Publications", address = "Oxford", year = "1986", referred = "[Grie91a].", comments = "", keywords = "", abstract = "", } @Article{Duff74a, author = "R. Duffin", title = "On {Fourier}'s analysis of linear inequality systems", journal = "Mathematical Programming Study", volume = "1", number = "", year = "1974", pages = "71 -- 95", referred = "[Saar91a].", comment = "", keywords = "", abstract = "", } @Techreport{Eise68a, author = "Harry Eisenpress and Abel Bomberault", title = "Efficient Symbolic Differentiation using {PL/I-F}ormac", type = "Technical Report", institution = "IBM New York Scientific Research Center", address = "Yorktown Heights, NY 10598", year = "1968", number = "320 -- 2956", month = sep, referred = "[Char91a].", comments = "", keywords = "", abstract = "", } @Article{Engq80a, author = "Bjorn Engquist and Tom Smedsaas", title = "Automatic computer code generation for hyperbolic and parabolic differential equations", journal = "{SIAM} Journal of Scientific and Statistical Computing", year = "1980", volume = "1", number = "2", pages = "249 -- 259", month = jun, referred = "[Char91a].", comments = "", keywords = "", abstract = "", } @Book{Elli90a, author = "Margaret~A. Ellis and Bjarne Stroustrup", title = "The Annotated {C}++ Reference Manual", publisher = "Addison-Wesley", series = "", address = "Reading, MA", year = "1990", referred = "[Kalm91a].", comments = "", keywords = "", abstract = "", } @Article{Enri87a, author = "Wayne H. Enright and John D. Pryce", title = "Two {FORTRAN} Packages for Assessing Initial Value Methods", journal = "ACM Trans. Math. Software", volume = "13", number = "1", year = "1987", pages = "1 -- 22", referred = "", keywords = "", abstract = "", } @Book{Esco76a, author = "P. R. Escobal", title = "Methods of Orbit Determination", edition = "Second", publisher = "Robert E. Krieger Publishing", series = "", address = "", year = "1976", referred = "[Layn91a].", comments = "", keywords = "", abstract = "", } @Book{Evtu85a, author = "{\Yu}ri G. Evtushenko", title = "Numerical Optimization Techniques", publisher = "Optimization Software Inc.", series = "", address = "New York", year = "1985", referred = "[Evtu91a].", comments = "", keywords = "", abstract = "", } @Incollection{Evtu91a, author = "{\Yu}ri G. Evtushenko", title = "Automatic Differentiation Viewed from Optimal Control", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", year = "1991", editor = "Andreas Griewank and George F. Corliss", publisher = "SIAM", address = "Philadelphia, PA", pages = "", referred = "[Irim91a].", comment = "", keywords = "", abstract = "", } @Book{Evtu89b, author = "{\Yu}ri G. Evtushenko and Vladimir P. Mazourik", title = "Optimization Software", publisher = "Znanie", series = "", address = "Moscow", year = "1989", referred = "[Evtu91a].", note = "(In Russian).", comments = "", keywords = "", abstract = "", } @Incollection{Evtu89a, author = "{\Yu}ri G. Evtushenko and V. G. Zhadan", title = "New approaches in optimization techniques", booktitle = "Proceedings of the 14th IFIP Conference on System Modelling and Optimization", year = "1989", editor = "", publisher = "Springer Verlag", series = "Lecture Notes in Control and Information Science No. 143", address = "", pages = "23 -- 27", referred = "[Irim91a].", comment = "", keywords = "", abstract = "", } @Article{Fate69a, author = "Richard J. Fateman", title = "Optimal Code for Serial and Parallel Computation", journal = "Comm. ACM", year = "1969", volume = "12", number = "12", pages = "694 -- 695", month = dec, referred = "[Char91a].", comment = "Discusses Breuer's paper as it relates to symbolic algebra.", keywords = "", abstract = "", } @Techreport{Feld90a, author = "S. I. Feldman and David M. Gay and M. W. Maimone and N. L. Schryer", title = "A {Fortran}-to-{C} Converter", institution = "AT\&T Bell Laboratories", address = "Murray Hill, NJ 07974", month = "", year = "1990", type = "Computing Science Technical Report", number = "No. 149", referred = "[Gayd91a].", comment = "", keywords = "", abstract = "", } @Incollection{Feld83a, author = "S. I. Feldman and P. J. Weinberger", title = "A Portable {Fortran} 77 Compiler", booktitle = "Unix Programmer's Manual, Volume II", publisher = "Holt, Rinehart and Winston", series = "", address = "", year = "1983", referred = "[Gayd91a].", comments = "", keywords = "", abstract = "", } @Techreport{Fiel86a, author = "D. E. Fields and others", title = "{PRESTO-II}: {A} Low-Level Waste Environment Transport and Risk Assessment Code", institution = "Martin Marietta Energy Systems, Inc., Oak Ridge National Laboratory", year = "1986", type = "", number = "ORNL-5970", address = "Oak Ridge, TN 37830", referred = "[Horw91a].", comment = "", keywords = "", abstract = "", } @Phdthesis{Fisc90b, author = "Hans-C. Fischer", title = "Schnelle Automatische {Differentiation}, {Einsclie}{\ss}ungsmethoden und {Anwendungen}", school = "Univ. Karlsruhe", address = "", year = "1990", referred = "[Irim91a].", comment = "", keywords = "", abstract = "", } @Misc{Fisc91a, author = "Hans-C. Fischer", title = "Differentiation Arithmetic and Applications in {Pascal-XSC}", howpublished = "Poster presented at {SIAM} {Workshop} on {Automatic} {Differentiation}, {Breckenridge}, {CO}", month = jan, year = "1991", referred = "[Corl91a]; [Layn91a].", comments = "", keywords = "", abstract = "", } @Techreport{Fisc87a, author = "Herbert Fischer", title = "Automatic differentiation: {Fast} method to compute the scalar product of gradient and given vector", type = "Technical Report", number = "No. 105", institution = "Technische Universt{\"a}t M{\"u}nchen, Institut f{\"u}r Angewandte Mathematik und Statistik", year = "1987", referred = "[Fisc87b]; [Fisc87e].", comment = "", note = "Also appeared as Report 26, Schwerpunktprogramm der Deutschen Forschungsgemeinschaft Anwendunsbezogene Optimierung und Steurung", keywords = "Differentiation arithmetic.", abstract = "This method describes a technique of differentiation arithmetic which uses as one of the basic operations $a+b*c$. This allows the technique to be faster and use less space than the basic method.", } @Techreport{Fisc87b, author = "Herbert Fischer", title = "Automatic differentiation: {Fast} method to compute the quadratic form of {Hessian} matrix and given vector", type = "Technical Report", number = "No. 108", institution = "Technische Universt{\"a}t M{\"u}nchen, Institut f{\"u}r Angewandte Mathematik und Statistik", year = "1987", referred = "", comment = "", keywords = "Differentiation arithmetic.", abstract = "This method describes a technique of differentiation arithmetic which uses as one of the basic operations $a+b*c$. This allows the technique to be faster and use less space than the basic method.", } @Techreport{Fisc87c, author = "Herbert Fischer", title = "Automatic differentiation: {Fast} method to compute $f''(u)vv$ for given vector-valued $f$ and given $u$, $v$", type = "Technical Report", number = "", institution = "Technische Universt{\"a}t M{\"u}nchen, Institut f{\"u}r Angewandte Mathematik und Statistik", year = "1987", referred = "", comment = "", keywords = "Differentiation arithmetic.", abstract = "Consider calculating the function $f''(u)vv$ for a given vector-valued f and given u, v, by using the affine function $ w: R \rightarrow R^n $ with $w(t) = u + t*v$, and the function $\psi: E \subseteq R \rightarrow R^n$ with $\psi(t) = f(w(t))$. Obviously $\psi''(0)11 = f''(u)vv =$ the vector wanted. The paper exploits this fact to produce a fast method for computing $f''(u)vv$. Operation counts are given for both the usual method and the fast method.", } @Article{Fisc90a, author = "Herbert Fischer", title = "Automatic differentiation: {Parallel} computation of function, gradient and {Hessian} matrix", journal = "Parallel Computing", volume = "13", number = "", year = "1990", pages = "101 -- 110", referred = "[Bisc91a].", comment = "", abstract = "", } @Techreport{Fisc87d, author = "Herbert Fischer", title = "Berechnung des Gradienten mit Automatischen Differenzieren", type = "Technical Report", number = "No. 103B", institution = "Technische Universt{\"a}t M{\"u}nchen, Institut f{\"u}r Angewandte Mathematik und Statistik", month = dec, year = "1987", referred = "[Fisc87a]; [Fisc87e].", comment = "", keywords = "", abstract = "", } @Techreport{Fisc87e, author = "Herbert Fischer", title = "Automatic Differentiation: How to Compute the {Hessian} matrix", type = "Report", number = "No. 26", institution = "Schwerpunktprogramm der Deutschen Forschungsgemeinschaft Anwendunsbezogene Optimierung und Steurung", year = "1987", referred = "[Fisc87e].", comment = "", keywords = "", abstract = "", } @Incollection{Fisc91b, author = "Herbert Fischer", title = "Special Problems in Automatic Differentiation", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", year = "1991", editor = "Andreas Griewank and George F. Corliss", publisher = "SIAM", address = "Philadelphia, PA", pages = "", referred = "[Garc91a].", comment = "", keywords = "", abstract = "", } @Article{Fisc91c, author = "Herbert Fischer", title = "Automatic differentiation of the vector that solves a parametric linear system", journal = "J. of Computational and Applied Mathematics", volume = "35", number = "", month = "", year = "to appear", pages = "", referred = "[Fisc91b].", comment = "", keywords = "", abstract = "", } @Article{Fitc85a, author = "John Fitch", title = "Solving algebraic problems with {REDUCE}", journal = "J. of Symbolic Computation", pages = "211 -- 227", volume = "1", number = "2", month = jun, year = "1985", referred = "[Char91a].", comment = "", keywords = "", abstract = "", } @Article{Flaj87a, author = "P. Flajolet and J.-M. Steyaert", title = "A Complexity Calculus for Recursive Tree Algorithms", journal = "Mathematical Systems Theory", volume = "19", number = "", year = "1987", pages = "301 -- 331", referred = "[Gold91a].", comment = "", keywords = "", abstract = "", } @Techreport{Flaj90a, author = "P. Flajolet and P. Sipala and J.-M. Steyaert", title = "Analytic Variations on the Common Subexpression Problem", institution = "INRIA-Rocquencourt", year = "1990", type = "Rapports de Recherche", number = "1210", address = "78153 Le Chesnay Cedex, France", referred = "[Gold91a].", comment = "", keywords = "", abstract = "", } @Book{Flan84a, author = "Harley Flanders", title = "Scientific Pascal", publisher = "Prentice-Hall", series = "", address = "Englewood Cliffs, NJ", year = "1984", referred = "[Flan91a].", comments = "", keywords = "", abstract = "", } @Incollection{Flan91a, author = "Harley Flanders", title = "Automatic Differentiation of Composite Functions", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", year = "1991", editor = "Andreas Griewank and George F. Corliss", publisher = "SIAM", address = "Philadelphia, PA", pages = "", referred = "", comment = "", keywords = "", abstract = "", } @Misc{Flan91b, author = "Harley Flanders", title = "Response to electronic mail survey", howpublished = "Personal communication", month = mar, year = "1991", referred = "[Jued91a].", comment = "", keywords = "", abstract = "", } @Article{Flet65a, author = "R. Fletcher", title = "Function Minimization Without Evaluating Derivatives --- {A} Review", journal = "Comput. J.", volume = "8", number = "", month = "", year = "1983", pages = "33 -- 41", referred = "[Gayd91a].", comment = "", keywords = "", abstract = "", } @Techreport{Flet91a, author = "R. Fletcher and J. A. J. Hall", title = "Ordering Algorithms for Irreducible Sparse Linear Systems", institution = "Dundee University", month = "", year = "1991", type = "Report", number = "NA/131", address = "Dundee, Scotland", referred = "[Dixo91a].", comment = "", keywords = "", abstract = "", } @Incollection{Fore89b, author = "Etienne Forest and Martin Berz", title = "Canonical Integration and Analysis of Periodic Maps using {Non}-{Standard} Analysis and {Lie} Methods", booktitle = "", year = "1989", editor = "", publisher = "Springer Verlag", address = "Berlin", pages = "47 -- 66", referred = "[Berz91a].", comment = "", keywords = "", abstract = "", } @Article{Fore89a, author = "Etienne Forest and Martin Berz and John Irwin", title = "Normal form methods for complicated periodic systems: {A} complete solution using differential algebra and {Lie} operators", journal = "Particle Accelerators", volume = "24", number = "", year = "1989", pages = "91 +", referred = "[Mich91a].", comment = "", keywords = "", abstract = "", } @Article{Four90a, author = "R. Fourer and David M. Gay and B. W. Kernighan", title = "A Modeling Language for Mathematical Programming", journal = "Management Science", volume = "36", number = "5", year = "1990", pages = "519 -- 554", referred = "[Gayd91a]; [Jued91a].", comments = "", keywords = "", abstract = "", } @Article{Foxp78a, author = "P. A. Fox and A. D. Hall and N. L. Schryer", title = "The {\tt PORT} Mathematical Subroutine Library", journal = "ACM Trans. Math. Software", volume = "4", number = "", month = jun, year = "1978", pages = "104 -- 126", referred = "[Gayd91a].", comment = "", keywords = "", abstract = "", } @Book{Fran78a, author = "P. M. Frank", title = "Introduction to System Sensitivity Theory", publisher = "Academic Press", series = "", address = "New York", year = "1978", referred = "[Worl91a].", comments = "", keywords = "", abstract = "", } @Techreport{Fras91a, author = "C. W. Fraser and D. R. Hanson", title = "A Retargetable Compiler for {ANSI} {C}", institution = "Department of Computer Science, Princeton University", month = feb, year = "1991", type = "Research Report", number = "CS--TR--303--91", address = "Princeton, NJ 08544", referred = "[Gayd91a].", comment = "", keywords = "", abstract = "", } @Article{Free88a, author = "Timothy Freeman and Gregory Imirzian and Erich Kaltofen and Lakshman Yagati", title = "Dagwood: {A} system of manipulating polynomials given by straight-line programs", journal = "ACM Trans. Math. Software", year = "1988", pages = "218 -- 240", volume = "14", month = sep, number = "3", referred = "[Char91a].", comments = "", keywords = "", abstract = "", } @Incollection{Garc79a, author = "Oscar Garc\'{\i}a", title = "Modelling stand development with stochastic differential equations", booktitle = "Mensuration for Management Planning of Exotic Forest Plantations", year = "1979", editor = "D. A. Elliot", publisher = "New Zealand Forest Service, FRI Symposium No. 20", address = "", pages = "315 -- 333", referred = "[Garc91a].", comment = "", keywords = "", abstract = "", } @Article{Garc83a, author = "Oscar Garc\'{\i}a", title = "A stochastic differential equation model for the height growth of forest stands", journal = "Biometrics", volume = "39", number = "", year = "1983", pages = "1059 -- 1072", referred = "[Garc91a].", keywords = "", abstract = "", } @Article{Garc84a, author = "Oscar Garc\'{\i}a", title = "New class of growth models for even-aged stands: {\it {Pinus} radiata} in {Golden} {Downs} {Forest}", journal = "New Zealand Journal of Forestry Science", volume = "14", number = "", year = "1984", pages = "65 -- 88", referred = "[Garc91a].", keywords = "", abstract = "", } @Incollection{Garc88a, author = "Oscar Garc\'{\i}a", title = "Experience with an advanced growth modelling methodology", booktitle = "Forest Growth Modelling and Prediction", year = "1988", editor = "A. R. Ek and S. R. Shifley and T. E. Burk", publisher = "USDA Forest Service, General Technical Report NC-120", address = "", pages = "668 -- 675", referred = "[Garc91a].", comment = "", keywords = "", abstract = "", } @Article{Garc88b, author = "Oscar Garc\'{\i}a", title = "Growth modelling -- {A} (re)view", journal = "New Zealand Forestry", volume = "33", number = "", year = "1988", pages = "14 -- 17", referred = "[Garc91a].", keywords = "", abstract = "", } @Incollection{Garc89a, author = "Oscar Garc\'{\i}a", title = "Growth Modelling -- {New} Developments", booktitle = "Japan and New Zealand Symposium on Forestry Management Planning", year = "1989", editor = "H. Nagumo and Y. Konohira", publisher = "Japan Association for Forestry Statistics", address = "", pages = "", referred = "[Garc91a].", keywords = "", abstract = "", } @Incollection{Garc91a, author = "Oscar Garc\'{\i}a", title = "A System for the Differentiation of {Fortran} Code and an Application to Parameter Estimation in Forest Growth Models", booktitle = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", year = "1991", editor = "Andreas Griewank and George F. Corliss", publisher = "SIAM", address = "Philadelphia, PA", pages = "", referred = "[Jued91a]; [Soul91a].", comment = "", keywords = "", abstract = "", } @Article{Gate85a, author = "B. L. Gates", title = "{GENTRAN}: {An} automatic code generation facility for {REDUCE}", journal = "ACM SIGSAM Bulletin", volume = "75", number = "", year = "1985", pages = " 24 -- 85", referred = "[Gold91a].", comment = "", keywords = "", abstract = "", } @Incollection{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 = "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 = "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",