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Algorithmic Differencing

  • Louis B. Rall
  • Thomas W. Reps

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.

Keywords

Arithmetic Operation Standard Function Divided Difference Symmetric Polynomial Automatic Differentiation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Louis B. Rall
    • 1
  • Thomas W. Reps
    • 1
  1. 1.University of Wisconsin-MadisonMadisonUSA

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