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Algorithmic Differencing

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Perspectives on Enclosure Methods

Abstract

An algorithmic representation of a function is a step-by-step specification of its evaluation in terms of known operations and functions, such as a computer program. In addition to function values, the algorithmic representation can be used to compute related quantities such as derivatives of the function. A process similar to automatie (or algorithmic) differentiation will be applied to obtain differences and divided differences of functions. Advantages of this approach are that it often reduces the sometimes catastrophic cancellation errors in computation of differences and divided differences and provides numerical convergence of divided differences to derivatives.

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Author information

Authors and Affiliations

  1. University of Wisconsin-Madison, 53706, Madison, WI, USA

    Louis B. Rall & Thomas W. Reps

Authors
  1. Louis B. Rall
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  2. Thomas W. Reps
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Editor information

Editors and Affiliations

  1. Universität Karlsruhe, Institut für Angewandte Mathematik, Deutschland

    Ulrich Kulisch , Rudolf Lohner  & Axel Facius ,  & 

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© 2001 Springer-Verlag Wien

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Rall, L.B., Reps, T.W. (2001). Algorithmic Differencing. In: Kulisch, U., Lohner, R., Facius, A. (eds) Perspectives on Enclosure Methods. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6282-8_7

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  • DOI: https://doi.org/10.1007/978-3-7091-6282-8_7

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83590-6

  • Online ISBN: 978-3-7091-6282-8

  • eBook Packages: Springer Book Archive

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