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Rigorous sensitivity analysis for systems of linear and nonlinear equations
Citation Link: https://doi.org/10.15480/882.318
Publikationstyp
Journal Article
Date Issued
1990
Sprache
English
Author(s)
Institut
TORE-DOI
Citation
Math. of Comp. 54 (10):721-736, 1990
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 the input data of which are afflicted with tolerances. The methods presented are very effective with the additional property that, due 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.
Subjects
Sensitivity analysis
linear and nonlinear systems
guaranteed bounds
inner inclusions
condition numbers
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