Andrii Dmytryshyn

activity

20172022

collaborators

5 papers

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…

math.SP2018

Generic symmetric matrix pencils with bounded rank

Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico

We show that the set of $n \times n$ complex symmetric matrix pencils of rank at most $r$ is the union of the closures of $⌊ r /2 ⌋ + 1$ sets of matrix pencils with some,…

math.RA2017

Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade

Andrii Dmytryshyn, Froilan M. Dopico

We show that the set of $m \times m$ complex skew-symmetric matrix polynomials of odd grade $d$ , i.e., of degree at most $d$ , and (normal) rank at most $2 r$ is the closure of the s…