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Structured eigenvalue backward errors of matrix pencils and polynomials with palindromic structures

Please always quote using this URN:urn:nbn:de:0296-matheon-13064
  • 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 significant difference between the backward errors with respect to structure preserving and arbitrary perturbations in many cases.

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Metadaten
Author:Christian Mehl
URN:urn:nbn:de:0296-matheon-13064
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2014/06/19
Release Date:2014/06/19
Tag:eigenvalue backward error; palindromic matrix pencil; palindromic matrix polynomial; perturbation theory; structured eigenvalue backward error
Institute:Technische Universität Berlin
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A18 Eigenvalues, singular values, and eigenvectors
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
Preprint Number:1067
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