Perturbation analysis for Hermitian, skew-Hermitian, H-even and H-odd matrix polynomials
Please always quote using this URN:urn:nbn:de:0296-matheon-7301
- We discuss the perturbation analysis for eigenvalues and eigenvectors of structured homogeneous matrix polynomials with Hermitian, skew-Hermitian, H-even and H-odd structure. We construct minimal structured perturbations (structured backward errors) such that an approximate eigenpair is an exact eigenpair of an appropriate perturbed structured matrix polynomial. We present various comparisons with unstructured backward errors and previous error bounds derived for the non-homogeneous case and show that our bounds present a significant improvement.
Author: | Sk. Safique Ahmad, Volker Mehrmann |
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URN: | urn:nbn:de:0296-matheon-7301 |
Referee: | Konrad Polthier |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2010/11/13 |
Release Date: | 2010/11/13 |
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: | 739 |