Structured eigenvalue backward errors of matrix pencils and polynomials with Hermitian and related structures
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- 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.
Verfasserangaben: | Bora Shreemayee, Karow Michael, Mehl Christian, Sharma Punit |
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URN: | urn:nbn:de:0296-matheon-12351 |
Gutachter*in: | Volker Mehrmann |
Dokumentart: | Preprint, Forschungszentrum Matheon |
Sprache: | Englisch |
Datum der Erstveröffentlichung: | 20.06.2013 |
Datum der Freischaltung: | 20.06.2013 |
Institut: | Technische Universität Berlin |
MSC-Klassifikation: | 15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A22 Matrix pencils [See also 47A56] |
Preprint-Nummer: | 1022 |