% File: corliss.bib 05 May 1999 % Publications of George F. Corliss % Refereed Journal Articles % @PHDTHESIS { Corliss1976a, AUTHOR = "George F. Corliss", TITLE = "Parallel Rootfinding Algorithms", SCHOOL = "Department of Mathematics, Michigan State University", YEAR = "1994", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1974a", COMMENTS = "", KEYWORDS = "", ABSTRACT = "", } % @ARTICLE { Corliss1976a, AUTHOR = "George F. Corliss", TITLE = "Computer Graphics Assisted Numerical Analysis Instruction", JOURNAL = "Computers and Graphics", VOLUME = "", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1976", PAGES = "11--13", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1976a", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1976b, AUTHOR = "George F. Corliss and Y. F. Chang", TITLE = "Three- and Five-Term Convergence Tests", BOOKTITLE = "Proceedings of the Sixth Conference on Numerical Mathematics and Computing (Winnipeg)", EDITOR = "", PUBLISHER = "University of Manitoba", ADDRESS = "Winnipeg", YEAR = "1976", PAGES = "135--153", ISBN = "", COMMENT = "", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1976b", KEYWORDS = "", ABSTRACT = "", } % @ARTICLE { Corliss1977a, AUTHOR = "George F. Corliss", TITLE = "Which Root Does the Bisection Algorithm Find?", JOURNAL = "SIAM Reviews", VOLUME = "", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1977", PAGES = "325--327", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1977a", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @ARTICLE { Corliss1977b, AUTHOR = "George F. Corliss and David Lowery", TITLE = "Choosing a Stepsize for {T}aylor Series Methods for Solving {ODE's}", JOURNAL = "J. Comp. \& Appl. Math.", VOLUME = "4", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1977", PAGES = "251--256", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1977b", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1977c, AUTHOR = "George F. Corliss", TITLE = "Integrating ODE's along Paths on Riemann Surfaces", BOOKTITLE = "Proceedings of the Seventh Conference on Numerical Mathematics and Computing (Winnipeg)", EDITOR = "", PUBLISHER = "University of Manitoba", ADDRESS = "Winnipeg", YEAR = "1977", PAGES = "279--296", ISBN = "", COMMENT = "", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1977c", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1978a, AUTHOR = "George F. Corliss and Y. F. Chang and John Fauss and Manuel Prieto", TITLE = "Convergence Analysis of Compound Taylor Series", BOOKTITLE = "Proceedings of the Eighth Manitoba Conference on Numerical Mathematics and Computing (Winnipeg)", EDITOR = "", PUBLISHER = "University of Manitoba", ADDRESS = "Winnipeg", YEAR = "1978", PAGES = "129--152", ISBN = "", COMMENT = "", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1978a", KEYWORDS = "", ABSTRACT = "", } % @ARTICLE { Corliss1980a, AUTHOR = "George F. Corliss", TITLE = "Integrating ODE's in the Complex Plane -- Pole Vaulting", JOURNAL = "Math. Comput.", VOLUME = "5", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1980", PAGES = "1181--1189", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1980a", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @ARTICLE { Chang1980b, AUTHOR = "Y. F. Chang and George F. Corliss", TITLE = "Ratio-like and Recurrence Relation Tests for Convergence of Series", JOURNAL = "J. Inst. Math. Appl.", VOLUME = "25", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1980", PAGES = "349--359", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1980b", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @ARTICLE { Chang1981a, AUTHOR = "Y. F. Chang and Michael Tabor and John Weiss and George F. Corliss", TITLE = "On the Analytic Structure of the {H}enon {H}eiles System", JOURNAL = "Phys. Letters A", VOLUME = "85", NUMBER = "4", ISSUE = "", MONTH = "", YEAR = "1981", PAGES = "211--213", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1981a", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @ARTICLE { Chang1982a, AUTHOR = "Y. F. Chang and George F. Corliss", TITLE = "Solving Ordinary Differential Equations Using {T}aylor Series", JOURNAL = "ACM Trans. Math. Software", VOLUME = "8", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1982", PAGES = "114--144", REFERRED = "MR 83g 65072.", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1982a", 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.", } % @ARTICLE { Corliss1983a, AUTHOR = "George F. Corliss", TITLE = "On Computing {D}arboux Type Series Analysis", JOURNAL = "Nonlinear Analysis, Theory, Methods \& Applications", VOLUME = "7", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1983", PAGES = "1247--1253", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1983a", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1983b, AUTHOR = "George F. Corliss", TITLE = "Using ADA as a Design Language - Classroom Experience", BOOKTITLE = "Proceedings of the ACM 1983 Annual Conference", EDITOR = "", PUBLISHER = "ACM", ADDRESS = "New York", YEAR = "1983", PAGES = "66--71", ISBN = "", COMMENT = "", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1983b", KEYWORDS = "", ABSTRACT = "", } % @ARTICLE { Corliss1984a, AUTHOR = "George F. Corliss", TITLE = "How is the Teaching of Software Engineering Related to the Teaching of {ADA}?", JOURNAL = "Journal of Pascal, Ada, \& Modula-2", VOLUME = "", NUMBER = "", ISSUE = "", MONTH = "May/June", YEAR = "1984", PAGES = "31--33", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1984a", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1984b, AUTHOR = "George F. Corliss and Louis B. Rall", TITLE = "Automatic Generation of {T}aylor Series in {P}ascal-{SC}: {B}asic Operations and Applications to Differential Equations", BOOKTITLE = "Trans. of the First Army Conference on Applied Mathematics and Computing (Washington, D.C., 1983)", PUBLISHER = "ARO Rep. 84-1, U. S. Army Res. Office", ADDRESS = "Research Triangle Park, N.C.", YEAR = "1984", PAGES = "177--209", REFERRED = "CMP 741 340.", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1984b", 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." } % @ARTICLE { Corliss1987a, AUTHOR = "George F. Corliss and Louis B. Rall", TITLE = "Adaptive, Self-Validating Numerical Quadrature", JOURNAL = "SIAM Journal on Scientific and Statistical Computing", VOLUME = "8", NUMBER = "5", ISSUE = "", MONTH = "", YEAR = "1987", PAGES = "831--847", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1987a", 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.", } % @ARTICLE { Corliss1987b, AUTHOR = "George F. Corliss", TITLE = "Design of {A}da Library of Elementary Functions with Error Handling", JOURNAL = "Journal on Pascal, Ada, and Modula-2", VOLUME = "6", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1987", PAGES = "", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1987b", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1987c, 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 = "Patrick Keast and Graeme Fairweather", PUBLISHER = "Reidel", ADDRESS = "Boston", YEAR = "1987", PAGES = "239--259", REFERRED = "Zbl. Math 615 -- 65018.", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1987c", COMMENT = "quadrature for integral iteration.", KEYWORDS = "interval quadrature; automatic differentiation.", ABSTRACT = "The interval implementation of Gaussian quadrature described in [Corliss1987a] 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 { Corliss1987d, AUTHOR = "George F. Corliss", TITLE = "Computing Narrow Inclusions for Definite Integrals", BOOKTITLE = "Computer Arithmetic: Scientific Computation and Programming Languages", EDITOR = "Edgar W. Kaucher and Ulrich Kulisch and Christian Ullrich", PUBLISHER = "Teubner", ADDRESS = "Stuttgart", YEAR = "1987", PAGES = "150--169", ISBN = "", COMMENT = "", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1987d", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Brown1987e, AUTHOR = "Ron Brown and George F. Corliss", TITLE = "Optimal Acceleration of the Bifilar Hybrid Step Motor with a Chopper Drive", BOOKTITLE = "Proceedings of the Sixteenth Annual Symposium on Incremental Motion Control Systems and Devices (Champaign)", EDITOR = "", PUBLISHER = "Incremental Motion Control Society", ADDRESS = "", YEAR = "1987", PAGES = "205--209", ISBN = "", COMMENT = "", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1987e", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1988a, AUTHOR = "George F. Corliss", TITLE = "Applications of Differentiation Arithmetic", BOOKTITLE = "Proceedings of the International Workshop on Reliability in Computing - The Role of Interval Methods in Scientific Computing (Columbus, 1987)", PUBLISHER = "Academic Press", EDITOR = "Ramon E. Moore", ADDRESS = "London", YEAR = "1988", PAGES = "127--148", ISBN = "0--12--505630--3", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1988a", 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." } % @ARTICLE { Corliss1989a, AUTHOR = "George F. Corliss", TITLE = "Survey of Interval Algorithms for Ordinary Differential Equations", JOURNAL = "Journal of Applied Mathematics and Computation", VOLUME = "31", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1989", PAGES = "112--120", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1989a", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @ARTICLE { Corliss1989b, AUTHOR = "George F. Corliss and Gary Krenz", TITLE = "Indefinite Integration with Validation", JOURNAL = "ACM Trans. Math. Software", VOLUME = "15", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1989", PAGES = "375--393", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1989b", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1990a, AUTHOR = "George F. Corliss", TITLE = "Industrial Applications of Interval Techniques", BOOKTITLE = "Computer Arithmetic and Self-Validating Numerical Methods", EDITOR = "Christian Ullrich", PUBLISHER = "Academic Press", ADDRESS = "New York", SERIES = "Notes and Reports in Mathematics in Science and Engineering, No. 7", YEAR = "1990", PAGES = "91--113", ISBN = "0-12-708245-X", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1990a", COMMENT = "", URL = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1991a, AUTHOR = "George F. Corliss and Louis B. Rall", TITLE = "Computing the Range of Derivatives", BOOKTITLE = "Computer Arithmetic, Scientific Computation, and Mathematical Modelling", EDITOR = "Edgar W. Kaucher and Svetoslav M. Markov and G{\"u}nter Mayer", PUBLISHER = "J. C. Baltzer", ADDRESS = "Basel", SERIES = "{IMACS} Annals on Computing and Applied Mathematics", VOLUME = "12", YEAR = "1991", PAGES = "195--212", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1991a", NOTE = "", COMMENT = "", KEYWORDS = "", ABSTRACT = "Evaluating the expression for a function $ f $ using interval arithmetic often yields overly pessimistic bounds for its range. We tighten bounds for the range of $ f $ and its derivatives by using a differentiation arithmetic for series generation. We apply monotonicity and Taylor form tests to each intermediate result of the calculation, not just to $ f $ itself. The resulting inclusions for the range of derivative values are several orders of magnitude tighter than bounds obtained from differentiation arithmetic and interval calculations alone.", } % @INCOLLECTION { Corliss1991b, AUTHOR = "George F. Corliss", TITLE = "Overloading Point and Interval {T}aylor Operators", BOOKTITLE = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", EDITOR = "Andreas Griewank and George F. Corliss", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, Penn.", YEAR = "1991", PAGES = "139--146", ISBN = "0--89871--284--X", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1991b", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1991c, AUTHOR = "George F. Corliss", TITLE = "Automatic Differentiation Bibliography", BOOKTITLE = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", EDITOR = "Griewank, Andreas and George F. Corliss", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, Penn.", YEAR = "1991", PAGES = "331--353", ISBN = "0--89871--284--X", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1991c", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1991d, AUTHOR = "George F. Corliss", TITLE = "Validated Anti-Derivatives", BOOKTITLE = "Computer Aided Proofs in Analysis (Cincinnati, 1989)", EDITOR = "Kenneth R. Meyer and Dieter S. Schmidt", PUBLISHER = "Springer-Verlag", ADDRESS = "New York", SERIES = "IMA Volumes in Mathematics and its Applications, No. 28", YEAR = "1991", PAGES = "90--96", ISBN = "", COMMENT = "", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1991d", KEYWORDS = "", ABSTRACT = "", } % @BOOK { Griewank1991e, EDITOR = "Andreas Griewank and George F. Corliss", TITLE = "Automatic Differentiation of Algorithms: Theory, Implementation, and Application", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, Penn.", YEAR = "1991", ISBN = "0--89871--284--X", URL = "www.eng.mu.edu/corlissg/Pubs/books.html#1991e", COMMENT = "Proceedings of the SIAM Workshop on the Automatic Differentiation of Algorithms in Breckenridge, Colorado, January 6 -- 8, 1991.", KEYWORDS = "", ABSTRACT = "" } % @ARTICLE { Bischof1992a, AUTHOR = "Christian Bischof and Alan Carle and George F. Corliss and Andreas Griewank and Paul Hovland", TITLE = "{ADIFOR}: Generating Derivative Codes from {F}ortran Programs, JOURNAL = "Scientific Computing", VOLUME = "1", NUMBER = "1", ISSUE = "", MONTH = "", YEAR = "1992", PAGES = "11--29", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1992a", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @ARTICLE { Bischof1992b, AUTHOR = "Christian Bischof and George F. Corliss and Larry Green and Andreas Griewank and Ken Haigler and Perry Newman", TITLE = "Automatic Differentiation of Advanced {CFD} Codes for Multidisciplinary Design", JOURNAL = "Journal on Computing Systems in Engineering", VOLUME = "3", NUMBER = "6", ISSUE = "", MONTH = "", YEAR = "1992", PAGES = "625--637", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1992b", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corless1992c, AUTHOR = "Robert M. Corless and George F. Corliss", TITLE = "Rationale for Guaranteed ODE Defect Control", BOOKTITLE = "Computer Arithmetic and Enclosure Methods", EDITOR = "Lidiya Atanassova and J{\"u}rgen Herzberger", PUBLISHER = "North-Holland", ADDRESS = "Amsterdam", YEAR = "1992", PAGE = "3--12", ISBN = "0444898344", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1992c", NOTE = "Proceedings of SCAN 1991: International Symposium on Computer Arithmetic and Scientific Computing (Oldenburg)", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1992d, AUTHOR = "George F. Corliss and Y. F. Chang", TITLE = "G-Stop Facility in ATOMFT, a Taylor Series Ordinary Differential Equation Solver", BOOKTITLE = "Computational Ordinary Differential Equations", EDITOR = "Simeon Ola Fatunla", PUBLISHER = "University Press", ADDRESS = "Champaign, Ill.", YEAR = "1992", PAGES = "37--77", ISBN = "", COMMENT = "", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1992d", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1992e, AUTHOR = "George F. Corliss and Christian H. Bischof and Andreas Griewank and Stephen Wright and Thomas Robey", TITLE = "Automatic Differentiation for {PDE's} -- Unsaturated Flow Case Study", BOOKTITLE = "Advances in Computer Methods for Partial Differential Equations -- VII", YEAR = "1992", EDITOR = "Robert Vichnevetshi and Doyle Knight and Gerard Richter", PUBLISHER = "IMACS", ADDRESS = "New Brunswick", PAGES = "150--156", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1992e", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INPROCEEDINGS { Bischof1992f, AUTHOR = "Christian H. Bischof and Alan Carle and George F. Corliss and Andreas Griewank", TITLE = "{ADIFOR}: {A}utomatic Differentiation in a Source Translation Environment", BOOKTITLE = "Proceedings of the International Symposium on Symbolic and Algebraic Computation", EDITOR = "Paul S. Wang", PUBLISHER = "ACM Press", ADDRESS = "New York", PAGES = "294--302", YEAR = "1992", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1992f", COMMENT = "Also appeared as Preprint MCS--P288--0192, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., January, 1992.", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Kirlinger1992g, AUTHOR = "Gabriella Kirlinger and George F. Corliss", TITLE = "On Implicit Taylor Series Methods for Stiff ODEs", BOOKTITLE = "Computer Arithmetic and Enclosure Methods", EDITOR = "Lidiya Atanassova and J{\"u}rgen Herzberger", PUBLISHER = "North-Holland", ADDRESS = "Amsterdam", YEAR = "1992", PAGE = "", ISBN = "0444898344", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1992g", NOTE = "Proceedings of SCAN 1991: International Symposium on Computer Arithmetic and Scientific Computing (Oldenburg)", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @ARTICLE { Bischof1993a, AUTHOR = "Christian Bischof and George F. Corliss and Andreas Griewank", TITLE = "Structured Second- and Higher-Order Derivatives through Univariate {T}aylor Series", JOURNAL = "Optimization Methods and Software", VOLUME = "2", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1993", PAGES = "211--232", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1993a", COMMENT = "Also appeared as Mathematics and Computer Science Division, Argonne National Laboratory Preprint MCS--P296--0392.", KEYWORDS = "", ABSTRACT = "", } % @ARTICLE { Griewank1993b, AUTHOR = "Andreas Griewank and Christian Bischof and Alan Carle and George F. Corliss and Karen Williamson", TITLE = "Derivative Convergence for Iterative Equation Solvers", JOURNAL = "Optimization Methods and Software", VOLUME = "2", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1993", PAGES = "321--355", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1993b", COMMENT = "", KEYWORDS = "Derivative convergence, automatic differentiation, implicit functions, preconditioning, Newton-like methods, secant updates.", ABSTRACT = "When nonlinear equation solvers are applied to parameter-dependent problems, their iterates can be interpreted as functions of these variable parameters. If they exist, the derivatives of these iterated functions can be recursively evaluated by the forward mode of automatic differentiation. Then one may ask whether and how fast these derivative values converge to the derivative of the implicit solution function, which may be needed for parameter identification, sensitivity studies, or design optimization. It is shown here that derivative convergence is achieved with an R-linear or possibly R-superlinear rate for a large class of memory-less contractions or secant updating methods. For a wider class of multi-step contractions, we obtain R-linear convergence of a simplified derivative updating scheme, which is more economical and can be easily generalized to second higher derivatives. We also formulate a constructive criterion for derivative convergence based on the implicit function theorem. All theoretical results are confirmed by numerical experiments on small test examples.", } % @ARTICLE { Chang1994a, AUTHOR = "Y. F. Chang and George F. Corliss", TITLE = "{ATOMFT}: {S}olving {ODEs} and {DAEs} Using {T}aylor Series", JOURNAL = "Computers and Mathematics with Applications", VOLUME = "28", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1994", PAGES = "209--233", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1994a", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1995a, AUTHOR = "Corliss, George F.", TITLE = "Guaranteed Error Bounds for Ordinary Differential Equations", EDITOR = "M. Ainsworth and J. Levesley and W. A. Light and M. Marletta", BOOKTITLE = "Theory of Numerics in Ordinary and Partial Differential Equations", PUBLISHER = "Oxford University Press", ADDRESS = "Oxford", YEAR = "1995", PAGES = "1--75", ISBN = "0198511930", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1995a", NOTE = "Lecture notes for a sequence of five lectures at the VI-th SERC Numerical Analysis Summer School, Leicester University, 25 - 29 July, 1994. COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @ARTICLE { Corliss1996a, AUTHOR = "George F. Corliss and Weldon A. Lodwick", TITLE = "Correct Computation of Solutions of Differential Algebraic Control Equations", JOURNAL = "Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik (ZAMM)", VOLUME = "", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "1996", PAGES = "37--40", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1996a", NOTES = "Special issue ``Numerical Analysis, Scientific Computing, and Computer Science''", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1996b, AUTHOR = "George F. Corliss and Robert Rihm", TITLE = "Validating an A Priori Enclosure Using High-Order {T}aylor Series", EDITOR = "G{\"o}tz Alefeld and Andreas Frommer and Bruno Lang", BOOKTITLE = "Scientific Computing and Validated Numerics: Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics - SCAN '95", PUBLISHER = "Akademie Verlag", ADDRESS = "Berlin", YEAR = "1996", ISBN = "3055017374 ", PAGES = "228--238", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1996b", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @BOOK { Berz1996c, EDITOR = "Martin Berz and Christian Bischof and George F. Corliss and Andreas Griewank", TITLE = "Computational Differentiation: Techniques, Applications, and Tools", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, Penn.", YEAR = "1996", ISBN = "", URL = "www.eng.mu.edu/corlissg/Pubs/books.html#1996c", COMMENT = "Proceedings of the SIAM Computational Differentiation Workshop, Santa Fe, New Mexico, February 12 - 15, 1996.", KEYWORDS = "", ABSTRACT = "" } % @INCOLLECTION { Rall1996d, AUTHOR = "Louis B. Rall and George F. Corliss", TITLE = "An Introduction to Automatic Differentiation", BOOKTITLE = "Computational Differentiation: Techniques, Applications, and Tools", EDITOR = "Martin Berz and Christian H. Bischof and George F. Corliss and Andreas Griewank", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, Penn.", YEAR = "1996", PAGES = "1--17", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1996d", COMMENT = "Also Marquette University Department of Mathematics, Statistics, and Computer Science Technical Report no. 434, Milwaukee, Wisc., July, 1996.", KEYWORDS = "Code list, forward mode, reverse mode, source code transformation, operator overloading.", ABSTRACT = " This paper provides a gentle introduction to the field of automatic differentiation (AD), with the goal of equipping the reader for the other papers in this book. AD is the systematic application of the familiar rules of calculus to computer programs, yielding programs for the propagation of numerical values of first, second, or higher derivatives. AD can be regarded as traversing the code list (or computational graph) in the forward mode, the reverse mode, or a combination of the two. Algorithms for numerical optimization, differential equations, and interval analysis all could use AD technology to compute the required derivatives. AD typically is implemented by using either source code transformation or operator overloading. We give examples of code for each. Finally, we outline some pitfalls of AD for naive users, and we present opportunities for future research.", } % @INCOLLECTION { Yang1996e, AUTHOR = "Wenhong Yang and George Corliss", TITLE = "Bibliography of Computational Differentiation", BOOKTITLE = "Computational Differentiation: Techniques, Applications, and Tools", EDITOR = "Martin Berz and Christian H. Bischof and George F. Corliss and Andreas Griewank", PUBLISHER = "SIAM", ADDRESS = "Philadelphia, Penn.", YEAR = "1996", PAGES = "393--418", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1996e", COMMENT = "Also Marquette University Department of Mathematics, Statistics, and Computer Science Technical Report no. 435, Milwaukee, Wisc., July, 1996.", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1996f, AUTHOR = "George F. Corliss", TITLE = "Where Is Validated {ODE} Solving Going?", BOOKTITLE = "Proceedings of the IMACS-GAMM International Symposium on Numerical Methods and Error Bounds", EDITOR = "J{\"u}rgen Herzberger", PUBLISHER = "Akademie Verlag", ADDRESS = "Berlin", YEAR = "1996", PAGES = "48--57", ISBN = "", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1996f", COMMENT = "Presented at IMACS-GAMM International Symposium on Numerical Methods and Error-Bounds, Universit{\"a}t Oldenburg, July 9--12, 1995.", KEYWORDS = "", ABSTRACT = " We discuss open problems in the field of initial value problems in ordinary differential equations to stimulate and focus research in this area and to attract additional workers to the field. We focus primarily on issues related to Lohner's AWA program.", } % @INCOLLECTION { Corliss1997a, AUTHOR = "George F. Corliss", TITLE = "Which Root Does the Bisection Algorithm Find?", BOOKTITLE = "Mathematical Modeling: Classroom Notes in Applied Mathematics", EDITOR = "Murray S. Klamkin", PUBLISHER = "SIAM", ADDRESS = "Philadelphia", YEAR = "1997", PAGES = "186--188", ISBN = "", COMMENT = "", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1997a", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Griewank1997b, AUTHOR = "Andreas Griewank and George F. Corliss and Petra Henneberger and Gabriella Kirlinger and Florian A. Potra and Hans J. Stetter", TITLE = "High-Order Stiff {ODE} Solvers via Automatic Differentiation and Rational Prediction", BOOKTITLE = "Numerical Analysis and Its Applications", SERIES = "Lecture Notes in Computer Science, No. 1196", YEAR = "1997", EDITOR = "", PUBLISHER = "Springer", ADDRESS = "Berlin", PAGES = "114--125", COMMENTS = "", KEYWORDS = "", ABSTRACT = "", } % @INPROCEEDINGS { Chin1998a, AUTHOR = "Paulina Chin and Robert M. Corless and George F. Corliss", TITLE = "Optimization Strategies for the Floating-Point {GCD}", BOOKTITLE = "Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation", EDITOR = "Oliver Gloor", PUBLISHER = "ACM Press", ADDRESS = "New York", YEAR = "1998", PAGES = "228--235", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1998a", COMMENT = "", KEYWORDS = "", ABSTRACT = "We describe algorithms for computing the greatest common divisor (GCD) of two univariate polynomials with inexactly known coefficients. Assuming that an estimate for the GCD degree is available (e.g. using an SVD-based algorithm), we formulate and solve a nonlinear optimization problem in order to determine the ``best'' GCD. We discuss various issues related to the implementation of the algorithms and present some preliminary test results.", } % @ARTICLE { Corliss1999a, AUTHOR = "George F. Corliss and R. Baker Kearfott", TITLE = "Rigorous Global Search: {I}ndustrial Applications", JOURNAL = "Reliable Computing", VOLUME = "", NUMBER = "", ISSUE = "", MONTH = "", YEAR = "to appear", PAGES = "", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1999a", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1999b, AUTHOR = "George F. Corliss", TITLE = "{SCAN-98} Collected Bibliography", BOOKTITLE = "Developments in Reliable Computing", YEAR = "1999", EDITOR = "Tibor Csendes", PUBLISHER = "Kluwer", ADDRESS = "Dordrecht, Netherlands", PAGES = "383--402", REFERRED = "", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1999b", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Corliss1999c, AUTHOR = "George F. Corliss and Louis B. Rall", TITLE = "Bounding Derivative Ranges", BOOKTITLE = "Encyclopedia of Optimization", SERIES = "", YEAR = "1999", EDITOR = "Panos M. Pardalos and C. A. Floudas", PUBLISHER = "Kluwer", ADDRESS = "Dordrecht", PAGES = "", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1999c", NOTE = "", KEYWORDS = "Interval arithmetic, automatic differentiation, Taylor series", ABSTRACT = "Interval arithmetic can be used to bound the range of a real function over an interval. Here, we bound the ranges of its Taylor coefficients (and hence derivatives) by evaluating it in an interval Taylor arithmetic. In the context of classical numerical methods, truncation errors, Lipschitz constants, or other constants related to existence or convergence assertions are often phrased in terms of bounds for certain derivatives. Hence, interval inclusions of Taylor coefficients can be used to give guaranteed bounds for quantities of concern to classical methods.", } % @INCOLLECTION { Rall1999d, AUTHOR = "Louis B. Rall and George F. Corliss", TITLE = "Automatic Differentiation: Point and Interval", BOOKTITLE = "Encyclopedia of Optimization", SERIES = "", YEAR = "1999", EDITOR = "Panos M. Pardalos and C. A. Floudas", PUBLISHER = "Kluwer", ADDRESS = "Dordrecht", PAGES = "", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1999d", NOTE = "", KEYWORDS = "", ABSTRACT = "", } % @INCOLLECTION { Walters1999e, AUTHOR = "James B. Walters and George F. Corliss", TITLE = "Automatic Differentiation: Point and Interval Taylor Operators", BOOKTITLE = "Encyclopedia of Optimization", SERIES = "", YEAR = "1999", EDITOR = "Panos M. Pardalos and C. A. Floudas", PUBLISHER = "Kluwer", ADDRESS = "Dordrecht", PAGES = "", URL = "www.eng.mu.edu/corlissg/Pubs/chapt.html#1999e", NOTE = "", KEYWORDS = "Automatic differentiation, code list, interval arithmetic, overloaded operator, Taylor series.", ABSTRACT = "Frequently of use in optimization problems, automatic differentiation may be used to generate Taylor coefficients. Specialized software tools generate Taylor series approximations, one term at a time, more efficiently than the general AD software used to compute (partial) derivatives. Through the use of operator overloading, these tools provide a relatively easy-to-use interface that minimizes the complications of working with both point and interval operations.", } % @ARTICLE { Nedialkov1999f, AUTHOR = "Ned S. Nedialkov and Ken R. Jackson and George F. Corliss", TITLE = "Validated Solutions of Initial Value Problems for Ordinary Differential Equations", JOURNAL = "Appl. Math. \& Comp.", VOLUME = "105", NUMBER = "1", ISSUE = "", MONTH = "", YEAR = "to appear", PAGES = "21--68", URL = "www.eng.mu.edu/corlissg/Pubs/journ.html#1999f", COMMENT = "http://www.elsevier.nl:80/inca/publications/store/5/2/2/4/8/2/?menu=cont&label=table", KEYWORDS = "", ABSTRACT = "", } % @INPROCEEDINGS { Feng1999g, AUTHOR = "Xin Feng and Richard Kelnhofer and George F. Corliss", TITLE = "A New Interval Bounding Algorithm for Parameter Estimation from Bounded Error Data", BOOKTITLE = "Proceedings of IFAC '99: 14th World Congress of International Federation of Automatic Control (Beijing, China, July 1999)", EDITOR = "", PUBLISHER = "IFAC", ADDRESS = "", YEAR = "1999", PAGES = "", URL = "", COMMENT = "", KEYWORDS = "", ABSTRACT = "", } %