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On some topological properties of numerical algorithms

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Abstract

A result quantity in a numerical algorithm is considered as a function of the input data, roundoff and truncation errors. In order to investigate this functional relationship using the methods of mathematical analysis a structural model of the numerical algorithm calledR-automaton is introduced. It is shown that the functional dependence defined by anR-automaton is a continuous rational function in a neighborhood of any data point except in a point set, the Lebesgue measure of which is zero. An effective general-purpose algorithm is presented to compute the derivative of any result quantity with respect to the individual roundoff and truncation errors. Some ways of generalizing theR-automation model without losing the results achieved are finally suggested.

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Authors and Affiliations

  1. Computer Science Department, University of Helsinki, Töölönkatu 11, SF-00100, Helsinki 10, Finland

    Martti Tienari

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  1. Martti Tienari
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Tienari, M. On some topological properties of numerical algorithms. BIT 12, 409–433 (1972). https://doi.org/10.1007/BF01932311

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  • DOI: https://doi.org/10.1007/BF01932311

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