Optimal Implementation of Differentiation Arithmetic.

Abstract

Differentiation arithmetic is an ordered-pair arithmetic which evaluates both the value and derivative of functions defined by formulas or subroutines, without symbolics or approximations. As in the case of complex arithmetic, multiplication and division are defined in terms of several real operations. Algorithms are given for evaluation of these operations with the same accuracy as real multiplication and division, that is, to the closest floating-point number. The same kind of optimal implementation is described for Taylor arithmetic, which permits calculation of Taylor coefficients of arbitrary order for functions defined by formulas or subroutines. Keywords: Automatic differentiation; Optimal computer arithmetic. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1986
Accession Number
ADA167494

Entities

People

  • Louis B. Rall

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Arithmetic
  • Automatic
  • Coefficients
  • Complex Numbers
  • Complex Variables
  • Computers
  • Errors
  • Identities
  • Mathematics
  • Numbers
  • Numerical Analysis
  • Rational Functions
  • Real Numbers
  • Test And Evaluation
  • United States

Readers

  • Approximation Theory.
  • Computer Programming and Software Development.