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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Rigorous sensitivity analysis for systems of linear and nonlinear equations
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by Siegfried M. Rump PDF
Math. Comp. 54 (1990), 721-736 Request permission

Abstract:

Methods are presented for performing a rigorous sensitivity analysis of numerical problems with independent, noncorrelated data for general systems of linear and nonlinear equations. The methods may serve for the following two purposes. First, to bound the dependency of the solution on changes in the input data. In contrast to condition numbers, a componentwise sensitivity analysis of the solution vector is performed. Second, to estimate the true solution set for problems whose input data are subject to tolerances. The methods presented are very effective and have the additional property that, owing to an automatic error control mechanism, every computed result is guaranteed to be correct. Examples are given for linear systems, demonstrating that the computed bounds are in general very sharp. Interesting comparisons to traditional condition numbers are given.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 54 (1990), 721-736
  • MSC: Primary 65G10; Secondary 65G05, 65H10
  • DOI: https://doi.org/10.1090/S0025-5718-1990-1011445-5
  • MathSciNet review: 1011445