Andrii Dmytryshyn

activity

20172026

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5 papers · 1 filter

math.NA2026

Distance to nearest skew-symmetric matrix polynomials of bounded rank

Andrii Dmytryshyn, Froilán M. Dopico, Rakel Hellberg

We propose an algorithm that approximates a given matrix polynomial of degree $d$ by another skew-symmetric matrix polynomial of a specified rank and degree at most $d$ . The algori…

math.NA2023

Minimal rank factorizations of polynomial matrices

Andrii Dmytryshyn, Froilán Dopico, Paul Van Dooren

We investigate rank revealing factorizations of $m \times n$ polynomial matrices $P (λ)$ into products of three, $P (λ) = L (λ) E (λ) R (λ)$ , or two, $P (λ) = L (λ) R (λ)$ , polynomial matr…

math.NA2022

Generic eigenstructures of Hermitian pencils

Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico

We obtain the generic complete eigenstructures of complex Hermitian $n \times n$ matrix pencils with rank at most $r$ (with $r \leq n$ ). To do this, we prove that the set of such pen…

math.NA2020

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

Andrii Dmytryshyn

A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory results for linearizations need t…

math.NA2019

Generic symmetric matrix polynomials with bounded rank and fixed odd grade

Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico

We determine the generic complete eigenstructures for $n \times n$ complex symmetric matrix polynomials of odd grade $d$ and rank at most $r$ . More precisely, we show that the set…