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Abstract: In this paper, we investigate condition numbers of eigenvalue problems ofmatrix polynomials with nonsingular leading coefficients, generalizingclassical results of matrix perturbation theory. We provide a relation betweenthe condition numbers of eigenvalues and the pseudospectral growth rate. Weobtain that if a simple eigenvalue of a matrix polynomial is ill-conditioned insome respects, then it is close to be multiple, and we construct an upper boundfor this distance measured in the euclidean norm. We also derive a newexpression for the condition number of a simple eigenvalue, which does notinvolve eigenvectors. Moreover, an Elsner-like perturbation bound for matrixpolynomials is presented.



Autor: Nikolaos Papathanasiou, Panayiotis Psarrakos

Fuente: https://arxiv.org/







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