Publication: Applications of Software for Automatic Differentiation in Numerical Computation
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Applications of Software for Automatic Differentiation in Numerical Computation

- incollection -
 

Author(s)
Louis B. Rall

Published in
Fundamentals of Numerical Computation (Computer Oriented Numerical Analysis)

Editor(s)
Götz Alefeld, R. D. Grigorieff

Year
1980

Publisher
Springer-Verlag

Abstract
Rall outlines generation of a code list, adding operations to the code list to compute derivatives or partial derivatives, and the automatic generation of Taylor series. He surveys the work in these areas done at the University of Wisconsin roughly between 1960 and 1980. Automatic differentiation can be applied to ordinary differential equations for either Taylor series or Lie series solutions. The use of automatic differentiation in nonlinear systems, nonlinear functionals, analysis of roundoff errors (sensitivity analysis), computational validation of existence and uniqueness, and quadrature is surveyed. This paper is a good summary of [Rall81a].

BibTeX
@INCOLLECTION{
         Rall1980AoS,
       AUTHOR = "Louis B. Rall",
       TITLE = "Applications of Software for Automatic Differentiation in Numerical Computation",
       BOOKTITLE = "Fundamentals of Numerical Computation (Computer Oriented Numerical Analysis)",
       PUBLISHER = "Springer-Verlag",
       ADDRESS = "Berlin",
       SERIES = "Computing Supplement No. 2",
       EDITOR = "G{\"o}tz Alefeld and R. D. Grigorieff",
       YEAR = "1980",
       PAGES = "141--156",
       REFERRED = "[Rall1996AIt].",
       COMMENT = "In [Alef80a]. Also appeared as {\sl MRC Technical Summary Report No.
         1976,\/} Mathematics Research Center, University of Wisconsin - Madison (1979).",
       KEYWORDS = "automatic differentiation; Taylor series; Lie series.",
       ABSTRACT = "Rall outlines generation of a code list, adding operations to the code list to
         compute derivatives or partial derivatives, and the automatic generation of Taylor series. He
         surveys the work in these areas done at the University of Wisconsin roughly between 1960 and 1980.
         Automatic differentiation can be applied to ordinary differential equations for either Taylor series
         or Lie series solutions. The use of automatic differentiation in nonlinear systems, nonlinear
         functionals, analysis of roundoff errors (sensitivity analysis), computational validation of
         existence and uniqueness, and quadrature is surveyed. This paper is a good summary of [Rall81a]."
}


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