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An efficient stochastic method for round-off error analysis

  • J. Vignes
  • R. Alt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 235)

Abstract

This paper presents a survey of research results obtained by the authors and by their team, on the round-off error propagation and the accuracy of mathematical computations.

The efficiency of the Permutation-Perturbation method is shown:
  1. i)

    For evaluating the accuracy of the exact finite method results,

     
  2. ii)

    For breaking off the iterative processes using the optimum termination criterion and evaluating the accuracy of the results,

     
  3. iii)

    For choosing the optimum integration step in approximate methods, such as the finite difference method.

     

The Permutation-Perturbation method may be also used to evaluate the data error propagation.

Examples are presented to illustrate the efficiency of the method.

Keywords

Truncation Error Local Truncation Error Arithmetic Operator Linear Differential System Quadruple Precision 
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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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • J. Vignes
    • 1
    • 2
  • R. Alt
    • 1
  1. 1.Paris Cedex 05France
  2. 2.Conseiller Scientifique à l'Institut Français du PétroleRueil-MalmaisonFrance

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