An error bound for approximate eigenvalues of a complex n-dimensional pencil (A, B) is given. From our theorem several well-known bounds follow as corollaries. Our result takes into account the general residual AX -BXW, where X ~ C n x m and W ~ C mxm with m ~< n.
Residual error bounds of generalized eigenvalue systems
β Scribed by Zhi-hao Cao
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 339 KB
- Volume
- 93
- Category
- Article
- ISSN
- 0024-3795
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β¦ Synopsis
A backward error analysis of approximate deflation pair systems of generalized eigenvalue problem is presented. The perturbation matrices obtained can be expressed by the residuals of the approximate deflation pair systems. Therefore, the corresponding error bounds with respect to the Frobenius norm and the spectral norm are computable.
π SIMILAR VOLUMES
We develop a simple oscillation theory for singular Sturm -Liouville problems and combine it with recent asymptotic results, and with the AWA interval-arithmetic code for integration of initial value problems with guaranteed error bounds, to obtain eigenvalue approximations with guaranteed error bou