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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.

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Metadaten
Author:Bora Shreemayee, Karow Michael, Mehl Christian, Sharma Punit
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
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