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Main Title: Structured eigenvalue backward errors of matrix pencils and polynomials with palindromic structures
Author(s): Bora, Shreemayee
Karow, Michael
Mehl, Christian
Sharma, Punit
Type: Article
Language Code: en
Abstract: We derive formulas for the backward error of an approximate eigenvalue of a *-palindromic matrix polynomial with respect to *-palindromic perturbations. Such formulas are also obtained for complex T-palindromic pencils and quadratic polynomials. When the T-palindromic polynomial is real, then we derive the backward error of a real number considered as an approximate eigenvalue of the matrix polynomial with respect to real T-palindromic perturbations. In all cases the corresponding minimal structure preserving perturbations are obtained as well. The results are illustrated by numerical experiments. These show that there is a significant difference between the backward errors with respect to structure preserving and arbitrary perturbations in many cases.
Issue Date: 2015
Date Available: 14-Dec-2017
DDC Class: 518 Numerische Analysis
512 Algebra
Subject(s): palindromic matrix pencil
palindromic matrix polynomial
perturbation theory
eigenvalue backward error
structured eigenvalue backward error
Journal Title: SIAM Journal on Matrix Analysis and Applications
Publisher: Society for Industrial and Applied Mathematics
Publisher Place: Philadelphia, Pa.
Volume: 36
Issue: 2
Publisher DOI: 10.1137/140973839
Page Start: 393
Page End: 416
EISSN: 1095-7162
ISSN: 0895-4798
Appears in Collections:FG Numerische Lineare Algebra » Publications

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