Backward errors for eigenvalues and eigenvectors of Hermitian, skew-Hermitian, H-even and H-odd matrix polynomials

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 eigenvalue and eigenvecto...

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Bibliographic Details
Published in:Linear & multilinear algebra 2013-09, Vol.61 (9), p.1244-1266
Main Authors: Ahmad, Sk. Safique, Mehrmann, Volker
Format: Article
Language:English
Subjects:
Approximation
backward error
Construction
Eigenvalues
Eigenvectors
Errors
H-even matrix polynomial
H-odd matrix polynomial
Hermitian matrix polynomial
homogeneous polynomial
Markov analysis
Mathematical analysis
nonlinear eigenvalue problem
perturbation analysis
Perturbation methods
Polynomials
skew-Hermitian matrix polynomial
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Summary: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 eigenvalue and eigenvector pair (finite or infinite eigenvalues) is an exact eigenvalue eigenvector pair of an appropriately perturbed structured matrix polynomial. We present various comparisons with unstructured backward errors and previous backward errors constructed for the non-homogeneous case and show that our results generalize previous results.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2012.746331