An ODE-based method for computing the Approximate Greatest Common Divisor of polynomials.

Antonio Fazzi, N. Guglielmi , Ivan Markovsky

Research output: Contribution to journalArticle

6 Citations (Scopus)
13 Downloads (Pure)

Abstract

Computing the greatest common divisor of a set of polynomials is a problem which plays an important role in different fields, such as linear system, control, and network theory. In practice, the polynomials are obtained through measurements and computations, so that their coefficients are inexact. This poses the problem of computing an approximate common factor. We propose an improvement and a generalization of the method recently proposed in Guglielmi et al. (SIAM J. Numer. Anal. 55, 1456–1482, 2017), which restates the problem as a (structured) distance to singularity of the Sylvester matrix. We generalize the algorithm in order to work with more than 2 polynomials and to compute an Approximate GCD (Greatest Common Divisor) of degree k ≥ 1; moreover, we show that the algorithm becomes faster by replacing the eigenvalues by the singular values.

Original languageEnglish
Pages (from-to)719-740
JournalNumerical Algorithms
Volume81
Issue number2
Early online date1 Jun 2018
DOIs
Publication statusPublished - 2018

Keywords

  • Approximate GCD
  • Iterative methods
  • Polynomials
  • Sylvester matrix

Fingerprint Dive into the research topics of 'An ODE-based method for computing the Approximate Greatest Common Divisor of polynomials.'. Together they form a unique fingerprint.

Cite this