Recovering a perturbation of a matrix polynomial from a perturbation of its linearization

Andrii Dmytryshyn

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arXiv · 2008.01794

Recovering a perturbation of a matrix polynomial from a perturbation of its linearization

Andrii Dmytryshyn

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Abstract

A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory results for linearizations need to be related back to matrix polynomials. In this paper we present an algorithm that finds which perturbation of matrix coefficients of a matrix polynomial corresponds to a given perturbation of the entire linearization pencil. Moreover we find transformation matrices that, via strict equivalence, transform a perturbation of the linearization to the linearization of a perturbed polynomial. For simplicity, we present the results for the first companion linearization but they can be generalized to a broader class of linearizations.

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Andrii Dmytryshyn. 2020-08-04. Recovering a perturbation of a matrix polynomial from a perturbation of its linearization. https://arxiv.org/abs/2008.01794

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