On computing root polynomials and minimal bases of matrix pencils

Vanni Noferini*, Paul Van Dooren

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
109 Downloads (Pure)

Abstract

We revisit the notion of root polynomials, thoroughly studied in (Dopico and Noferini, 2020 [9]) for general polynomial matrices, and show how they can efficiently be computed in the case of a matrix pencil λE+A. The method we propose makes extensive use of the staircase algorithm, which is known to compute the left and right minimal indices of the Kronecker structure of the pencil. In addition, we show here that the staircase algorithm, applied to the expansion (λ−λ0)E+(A−λ0E), constructs a block triangular pencil from which a minimal basis and a maximal set of root polynomials at the eigenvalue λ0, can be computed in an efficient manner.

Original languageEnglish
Pages (from-to)86-115
Number of pages30
JournalLinear Algebra and Its Applications
Volume658
DOIs
Publication statusPublished - 1 Feb 2023
MoE publication typeA1 Journal article-refereed

Keywords

  • Local Smith form
  • Matrix pencil
  • Maximal set
  • Minimal basis
  • Root polynomial
  • Smith form
  • Staircase algorithm

Fingerprint

Dive into the research topics of 'On computing root polynomials and minimal bases of matrix pencils'. Together they form a unique fingerprint.

Cite this