Generalized algorithms for the approximate matrix polynomial GCD of reducing data uncertainties with application to MIMO system and control

Antonio Fazzi, Nicola Guglielmi, Ivan Markovsky

Research output: Contribution to journalArticle

Abstract

Computation of (approximate) polynomials common factors is an important problem in several fields of science, like control theory and signal processing. While the problem has been widely studied for scalar polynomials, the scientific literature in the framework of matrix polynomials seems to be limited to the problem of exact greatest common divisor computation. In this paper, we generalize two algorithms from scalar to matrix polynomials. The first one is fast and simple. The second one is more accurate but computationally more expensive. We test the performances of the two algorithms and observe similar behavior to the one in the scalar case. Finally we describe an application to multi-input multi-output linear time-invariant dynamical systems.
Original languageEnglish
Article number113499
Number of pages25
JournalJournal of Computational and Applied Mathematics
Volume393
Publication statusPublished - Sep 2021

Keywords

  • Matrix polynomials
  • Approximate common factor
  • Subspace method
  • Matrix ODEs

Fingerprint Dive into the research topics of 'Generalized algorithms for the approximate matrix polynomial GCD of reducing data uncertainties with application to MIMO system and control'. Together they form a unique fingerprint.

Cite this