A Björck-Pereyra-type algorithm for Szegö-Vandermonde matrices based on properties of unitary Hessenberg matrices

Tom Bella, Yuli Eidelman, Israel Gohberg, Israel Koltracht, Vadim Olshevsky

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we carry over the Björck-Pereyra algorithm for solving Vandermonde linear systems to what we suggest to call Szegö-Vandermonde systems VΦ(x), i.e., polynomial-Vandermonde systems where the corresponding polynomial system Φ is the Szegö polynomials. The properties of the corresponding unitary Hessenberg matrix allow us to derive a fast O(n2) computational procedure. We present numerical experiments that indicate that for ill-conditioned matrices the new algorithm yields better forward accuracy than Gaussian elimination.

Original languageEnglish
Pages (from-to)634-647
Number of pages14
JournalLinear Algebra and Its Applications
Volume420
Issue number2-3
DOIs
StatePublished - 15 Jan 2007

Keywords

  • Bjorck-pereyra algorithm
  • Polynomial-Vandermonde matrices
  • Szegö polynomials
  • Unitary hessenberg matrices
  • Vandermonde matrices
  • fast algorithms

Fingerprint

Dive into the research topics of 'A Björck-Pereyra-type algorithm for Szegö-Vandermonde matrices based on properties of unitary Hessenberg matrices'. Together they form a unique fingerprint.

Cite this