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Title: Rigorous sensitivity analysis for systems of linear and nonlinear equations
Language: English
Authors: Rump, Siegfried M. 
Keywords: Sensitivity analysis;linear and nonlinear systems;guaranteed bounds;inner inclusions;condition numbers
Issue Date: 1990
Source: Math. of Comp. 54 (10):721-736, 1990
Abstract (english): 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.
DOI: 10.15480/882.318
Institute: Zuverlässiges Rechnen E-19 
Type: (wissenschaftlicher) Artikel
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