BIT Numerical Mathematics

, Volume 24, Issue 1, pp 92–101 | Cite as

Uncertainty in the solution of linear operator equations

  • Peter Linz
Part II Numerical Mathematics

Abstract

In this paper we introduce and explore the concept of uncertainty of an approximate solution of a linear operator equation. This uncertainty is a measure of the difference between a computed solution and other plausible answers. When the operator equation is wellposed, the uncertainty is closely related to the more traditional notion of the accuracy of an approximate solution. However, for illposed equations, the uncertainty concept gives a new way of looking at such problems and helps in assessing the meaning of the computed results.

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References

  1. 1.
    F. R. de Hoog,Review of Fredholm equations of the first kind, in R. S. Anderssen, F. R. de Hoog and M. A. Lukas (eds.)The Application and Numerical Solution of Integral Equations. Sijthoff and Noordhoff, Alphen aan den Rijn, 1980.Google Scholar
  2. 2.
    P. Linz,Theoretical Numerical Analysis, Wiley-Interscience, New York, 1979.Google Scholar
  3. 3.
    A. N. Tikhonov and V. Y. Arsenin,Solution of Ill-posed Problems, V. H. Winston, Washington, D.C. 1977.Google Scholar

Copyright information

© BIT Foundations 1984

Authors and Affiliations

  • Peter Linz
    • 1
  1. 1.Division of Computer ScienceUniversity of CaliforniaDavisUSA

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