Structured eigenvalue backward errors of matrix pencils and polynomials with Hermitian and related structures
Please always quote using this URN:urn:nbn:de:0296-matheon-12351
- We derive a formula for the backward error of a complex number $\lambda$ when considered as an approximate eigenvalue of a Hermitian matrix pencil or polynomial with respect to Hermitian perturbations. The same are also obtained for approximate eigenvalues of matrix pencils and polynomials with related structures like skew-Hermitian, $*$-even and $*$-odd. Numerical experiments suggest that in many cases there is a significant difference between the backward errors with respect to perturbations that preserve structure and those with respect to arbitrary perturbations.
Author: | Bora Shreemayee, Karow Michael, Mehl Christian, Sharma Punit |
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URN: | urn:nbn:de:0296-matheon-12351 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2013/06/20 |
Release Date: | 2013/06/20 |
Institute: | Technische Universität Berlin |
MSC-Classification: | 15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A22 Matrix pencils [See also 47A56] |
Preprint Number: | 1022 |