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Accurate Scientific Computations pp 183–205Cite as

An efficient stochastic method for round-off error analysis

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Part of the book series: Lecture Notes in Computer Science ((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.

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References

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Author information

Authors and Affiliations

  1. 4, Place Jussieu, 75230, Paris Cedex 05, France

    J. Vignes (Professeur à l'Université P. et M. Curie de Paris) & R. Alt (Maître de Conférence à l'Université P. et M. Curie de Paris)

  2. Conseiller Scientifique à l'Institut Français du Pétrole, 4, Avenue de Bois-Préau, 92500, Rueil-Malmaison, France

    J. Vignes (Professeur à l'Université P. et M. Curie de Paris)

Authors
  1. J. Vignes
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  2. R. Alt
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Editor information

Willard L. Miranker Richard A. Toupin

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© 1986 Springer-Verlag Berlin Heidelberg

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Vignes, J., Alt, R. (1986). An efficient stochastic method for round-off error analysis. In: Miranker, W.L., Toupin, R.A. (eds) Accurate Scientific Computations. Lecture Notes in Computer Science, vol 235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16798-6_12

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  • DOI: https://doi.org/10.1007/3-540-16798-6_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16798-3

  • Online ISBN: 978-3-540-47118-9

  • eBook Packages: Springer Book Archive

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