Publication: An Introduction to Automatic Differentiation
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An Introduction to Automatic Differentiation

- incollection -
 

Author(s)
Louis B. Rall , George F. Corliss

Published in
Computational Differentiation: Techniques, Applications, and Tools

Editor(s)
Martin Berz, Christian H. Bischof, George F. Corliss, Andreas Griewank

Year
1996

Publisher
SIAM

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.

Cross-References
Berz1996CDT

AD Theory and Techniques
General

BibTeX
@INCOLLECTION{
         Rall1996AIt,
       author = "Louis B. Rall and George F. Corliss",
       editor = "Martin Berz and Christian H. Bischof and George F. Corliss and Andreas Griewank",
       title = "An Introduction to Automatic Differentiation",
       booktitle = "Computational Differentiation: Techniques, Applications, and Tools",
       pages = "1--17",
       publisher = "SIAM",
       address = "Philadelphia, PA",
       key = "Rall1996AIt",
       crossref = "Berz1996CDT",
       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.",
       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.",
       referred = "[Braconnier2002FRE], [Christianson1996SSU], [Hoefkens2001EHO], [Klein2002DMf].",
       ad_theotech = "General",
       year = "1996"
}


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