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Etude statistique des erreurs dans l'arithmetique des ordinateurs; application au controle des resultats d'algorithmes numeriques

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Abstract

Since numerical calculations on a digital computer are performed on operands with a limited number of significant digits it follows that each operator in the computational arithmetic is merely an approximation of the corresponding mathematical operator.

Therefore every numerical operation carried out on a computer generates a numerical error.

The statistical evaluation of these errors is discussed in the first part of the paper. In the second part, the formulae obtained above are used to assess the validity of numerical results obtained in resolution of linear systems, algebraic equations and in matrix inversion.

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References bibliographiques

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Authors and Affiliations

  1. Institut Français du Pétrole, 1, 4 avenue de Bois-Préau, 92502, Rueil-Malmaison, France

    M. La Porte (Maître de Recherches)

  2. 4 place Jussieu, 75230, Paris-Cedex 05, France

    J. Vignes (Professeur à l'Université Paris VI)

Authors
  1. M. La Porte
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  2. J. Vignes
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La Porte, M., Vignes, J. Etude statistique des erreurs dans l'arithmetique des ordinateurs; application au controle des resultats d'algorithmes numeriques. Numer. Math. 23, 63–72 (1974). https://doi.org/10.1007/BF01409991

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  • DOI: https://doi.org/10.1007/BF01409991

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