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Structured eigenvalue conditioning and backward error of a class of polynomial eigenvalue problems

Please always quote using this URN:urn:nbn:de:0296-matheon-4299
  • Characterisations of simple eigenvalues of complex matrix polynomials with *-even/odd and *-palindromic/antipalindromic structures that have the same normwise condition number with respect to structure preserving and arbitrary perturbations are obtained. Here * denotes either the transpose T or the conjugate tranpose *. In the process we obtain formulae for the normwise structured condition number of simple eigenvalues of T-palindromic/antipalindromic and *-even/odd polynomials. Moreover, conditions under which the normwise structured backward error of approximate eigenvalues of such polynomials is equal to the unstructured error are also derived. These lead to complete characterisations of approximate eigenvalues that have the same structured and unstructured backward errors for the *-even/odd and T-even/odd polynomials.

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Metadaten
Author:Shreemayee Bora
URN:urn:nbn:de:0296-matheon-4299
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2007/04/12
Release Date:2007/04/12
Tag:
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
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F35 Matrix norms, conditioning, scaling [See also 15A12, 15A60]
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L15 Eigenvalue problems
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L20 Stability and convergence of numerical methods
Preprint Number:417
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