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Main Title: Structured eigenvalue backward errors of matrix pencils and polynomials with Hermitian and related structures
Author(s): Bora, Shreemayee
Karow, Michael
Mehl, Christian
Sharma, Punit
Type: Article
Language Code: en
Abstract: We derive a formula for the backward error of a complex number λ 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.
Issue Date: 17-Apr-2014
Date Available: 14-Dec-2017
DDC Class: 512 Algebra
518 Numerische Analysis
Subject(s): Hermitian matrix pencil
perturbation theory
eigenvalue backward error
structured mapping problem
Hermitian matrix polynomial
Journal Title: SIAM Journal on Matrix Analysis and Applications
Publisher: Society for Industrial and Applied Mathematics
Publisher Place: Philadelphia, Pa.
Volume: 35
Issue: 2
Publisher DOI: 10.1137/130925621
Page Start: 453
Page End: 475
EISSN: 1095-7162
ISSN: 0895-4798
Appears in Collections:FG Numerische Lineare Algebra » Publications

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