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Perturbation analysis for complex symmetric, skew symmetric, even and odd matrix polynomials

Please always quote using this URN:urn:nbn:de:0296-matheon-6831
  • In this work we propose a general framework for the structured perturbation analysis of several classes of structured matrix polynomials in homogeneous form, including complex symmetric, skew-symmetric, even and odd matrix polynomials. We introduce structured backward errors for approximate eigenvalues and eigenvectors and we construct minimal structured perturbations such that an approximate eigenpair is an exact eigenpair of an appropriately perturbed matrix polynomial. This work extends previous work for the non-homogeneous case (we include infinite eigenvalues) and we show that the structured backward errors improve the known unstructured backward errors.

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Metadaten
Author:Sk. Safique Ahmad, Volker Mehrmann
URN:urn:nbn:de:0296-matheon-6831
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2010/08/02
Release Date:2010/08/02
Tag:
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A12 Conditioning of matrices [See also 65F35]
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]
Preprint Number:689
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