Research Seminar in Mathematics - Recovering a perturbation of a matrix polynomial from a perturbation of its linearization

Speaker

Andrii Dmytryshyn, Örebro University

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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 the linearizations need to be related back to matrix polynomials. 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. We consider general matrix polynomials as well as polynomials of odd grade whose coefficients are (skew) symmetric. Moreover, we find transformation matrices that, via strict equivalence or, respectively, congruence, transform a perturbation of the linearization to the linearization of a perturbed polynomial.