Complexity of Derivatives Generated by Symbolic Differentiation

Herbert Fischer () and Hubert Warsitz
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Herbert Fischer: Technische Universität München, Fakultüt für Mathematik
Hubert Warsitz: Technische Universität München, Fakultüt für Mathematik

A chapter in Computer Algebra in Scientific Computing, 2000, pp 129-144 from Springer

Abstract: Abstract The computational solution of many mathematical problems involves derivatives. Programs for computing derivatives may be (1) hand-Coded, (2) set up via function calls and divided differences, or (3) obtained using symbolic differentiation. In practice, the divided differences approach is still the standard technique. But in many cases, derivatives can be computed cheaper and more accurately by symbolic differentiation. In this paper we investigate the complexity of algorithms for computing derivatives of rational functions. In particular, we deal with the forward mode and the reverse mode of symbolic differentiation. We discuss bounds on the amount of work within the described algorithms in terms of rational operations.

Keywords: Rational Function; Elementary Function; Reverse Mode; Jacobian Matrice; Stated Algorithm (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-57201-2_12

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DOI: 10.1007/978-3-642-57201-2_12

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