On backward errors of structured polynomial eigenproblems solved by structure preserving linearizations - Mathematics > Numerical AnalysisReportar como inadecuado




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Abstract: First, we derive explicit computable expressions of structured backwarderrors of approximate eigenelements of structured matrix polynomials includingsymmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials.We also determine minimal structured perturbations for which approximateeigenelements are exact eigenelements of the perturbed polynomials. Next, weanalyze the effect of structure preserving linearizations of structured matrixpolynomials on the structured backward errors of approximate eigenelements. Weidentify structure preserving linearizations which have almost no adverseeffect on the structured backward errors of approximate eigenelements of thepolynomials. Finally, we analyze structured pseudospectra of a structuredmatrix polynomial and establish a partial equality between unstructured andstructured pseudospectra.



Autor: Bibhas Adhikari, Rafikul Alam

Fuente: https://arxiv.org/







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