Speaker
Froilán M. Dopico
(Universidad Carlos III de Madrid (Spain))
Description
We propose an algorithm that approximates a given matrix polynomial of any degree $d$ by another matrix polynomial of a prescribed rank and degree at most $d$. The algorithm combines recent advances in the theory of generic factorizations for matrix polynomials of bounded rank and degree with an alternating least squares strategy. For $d=1$, the algorithm includes the important case of matrix pencils. The algorithm solves, as a particular case, the well-known problem of computing the distance to singularity of a regular matrix polynomial. We present numerical experiments for testing the proposed algorithm and for comparison to the previously known ones.
Authors
Andrii Dmytryshyn
(Chalmers University of Technology and University of Gothenburg (Sweden))
Froilán M. Dopico
(Universidad Carlos III de Madrid (Spain))
Marten Gulliksson
(Örebro University (Sweden))
Rakel Hellberg
(Chalmers University of Technology and University of Gothenburg (Sweden))
Sweta Das
(Örebro University (Sweden))