Volume 38, pp. 275-302, 2011.

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

Sk. Safique Ahmad and Volker Mehrmann


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 of Adhikari and Alam 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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Key words

Polynomial eigenvalue problem, even matrix polynomial, odd matrix polynomial, complex symmetric matrix polynomial, complex skew-symmetric matrix polynomial, perturbation theory, backward error.

AMS subject classifications

65F15, 15A18, 65F35, 15A12

ETNA articles which cite this article

Vol. 51 (2019), pp. 151-168 Sk. Safique Ahmad: Perturbation analysis for palindromic and anti-palindromic nonlinear eigenvalue problems
Vol. 52 (2020), pp. 370-390 Sk. Safique Ahmad and Prince Kanhya: Perturbation analysis on matrix pencils for two specified eigenpairs of a semisimple eigenvalue with multiplicity two

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