BIT Numerical Mathematics

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

On some topological properties of numerical algorithms

  • Martti Tienari


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.


Input Data Rational Function Computational Mathematic Lebesgue Measure Mathematical Analysis 
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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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