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Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides

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Abstract

In the spirit ofWilkinson's [1, 2] backward error analysis, conditions are established under which a given approximate solution of a system ofn linear equations withn unknowns is the exact solution of a modified system whose coefficients and right-hand sides are within a given neighborhood of those of the original system.

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References

  1. Wilkinson, J. H.: Error analysis of floating-point computation. Numerische Mathematik2, 319–340 (1960).

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  2. Wilkinson, J. H.: Rounding errors in algebraic processes. National Physical Laboratory, Notes on Applied Science No. 32, London, 1963.

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Authors and Affiliations

  1. IBM Zurich Research Laboratory Rüschlikon, Zürich, (Schweiz)

    W. Oettli & W. Prager

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  1. W. Oettli
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  2. W. Prager
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Oettli, W., Prager, W. Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides. Numer. Math. 6, 405–409 (1964). https://doi.org/10.1007/BF01386090

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  • DOI: https://doi.org/10.1007/BF01386090

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