Fraction-free computation of the unit-circle resultant with any singularity profile

Yuval Bistritz, Alexander Lifshitz

Research output: Contribution to journalArticlepeer-review

Abstract

We show that an algorithm established in a recent publication in this journal to provide a fraction-free version for the Bistritz test can also be used to compute the unit-circle resultant. The consequence is an effective new algorithm to find this resultant for any complex polynomial that is also an efficient integer algorithm for polynomial with real or Gaussian integer coefficients. The algorithm ends always with the resultant expressed as the minimal degree multivariate polynomial of the polynomial's (indeterminate) coefficients. A simpler form of the algorithm, that equally reaches this expression in all circumstances, but is not guaranteed to stay over integers during possible intermediate abnormal gaps, is also suggested along with the simplest form that the algorithm takes in the strongly regular case.

Original languageEnglish
Pages (from-to)377-393
Number of pages17
JournalLinear and Multilinear Algebra
Volume69
Issue number3
DOIs
StatePublished - 2021

Keywords

  • Sylvester matrix
  • T-Bezoutian
  • The Schur–Cohn problem
  • discrete-time linear systems stability
  • immittance algorithms
  • integer algorithm
  • subresultants
  • symmetric polynomials

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