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BIT Numerical Mathematics

, Volume 12, Issue 3, pp 409–433 | Cite as

On some topological properties of numerical algorithms

  • Martti Tienari
Article

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.

Keywords

Input Data Rational Function Computational Mathematic Lebesgue Measure Mathematical Analysis 
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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Copyright information

© BIT Foundations 1972

Authors and Affiliations

  • Martti Tienari
    • 1
  1. 1.Computer Science DepartmentUniversity of HelsinkiHelsinki 10Finland

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