A Björck-Pereyra-type algorithm for Szegö-Vandermonde matrices based on properties of unitary Hessenberg matrices
type: Item
instance of: scholarly article
title: A Björck-Pereyra-type algorithm for Szegö-Vandermonde matrices based on properties of unitary Hessenberg matrices
zbMATH Open document ID: 1111.65026
author: Y. Eidelman
author: I. Gohberg
author: Tom Bella
author: I. Koltracht
author: V. Olshevsky
published in: Linear Algebra and its Applications
publication date: 2007-01-09T00:00:00Z
review text: The paper presents a Björk-Pereyra-type algorithm to solve linear systems with a polynomial-Vandermonde \(n\times n \) matrix, where the corresponding polynomials are the Szegö polynomials. Such matrix is called the Szegö-Vandermonde matrix. The algorithm exploits the properties of the related unitary Hessenberg matrix to reduce the computational complexity \(O(n^2)\) operations which is in contrast to the usual \(O(n^3)\) complexity of standard structure ignoring methods. Numerical experiments indicate a good performance for ill-conditioned systems when comparing it with the Gaussian elimination.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 15A54
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 65F22
zbMATH DE Number: 5083631
zbMATH Keywords: Björk-Pereyra algorihm
zbMATH Keywords: Szegö polynomials
zbMATH Keywords: unitary Hessenberg matrices
zbMATH Keywords: polynomial Vandermonde matrices
zbMATH Keywords: fast algorithms
zbMATH Keywords: comparison of methods
zbMATH Keywords: computational complexity
zbMATH Keywords: numerical experiments
zbMATH Keywords: ill-conditioned systems
zbMATH Keywords: Gaussian elimination
reviewed by: Lubomír Bakule
MaRDI profile type: Publication
full work available at URL: j.laa.2006.08.032
OpenAlex ID: W2078755977
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DOI: 10.1016/J.LAA.2006.08.032
description: scientific article; zbMATH DE number 5083631