A new algorithm for computing the Geronimus transformation with large shifts
type: Item
instance of: scholarly article
title: A new algorithm for computing the Geronimus transformation with large shifts
zbMATH Open document ID: 1191.65039
author: Maria Isabel Bueno Cachadina
author: Alfredo Deaño
author: Edward Tavernetti
published in: Numerical Algorithms
publication date: 2010-05-19T00:00:00Z
review text: The authors consider the numerical computation of the Geronimus transformation with shift and parameter \(C\) of a Jacobi matrix. The numerical behavior of the available algorithms are investigated. The problem of computing the Geronimus transformation is proved to be very ill-conditioned when \(C\) is zero. The authors propose a new algorithm which is more accurate when the shift moves away from the support of the measure and \(C\) is nonzero. The forward errors of the algorithm is estimated and a backward error analysis of the algorithm is presented. Some numerical experiments are shown to illustrate that the method is componentwise forward stable.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 65Q30
Mathematics Subject Classification ID: 65F22
zbMATH DE Number: 5709204
zbMATH Keywords: Geronimus transformation
zbMATH Keywords: accuracy
zbMATH Keywords: roundoff error analysis
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: three-term recurrence relations
zbMATH Keywords: Jacobi matrix
zbMATH Keywords: ill-conditioned
zbMATH Keywords: algorithm
zbMATH Keywords: numerical experiments
describes a project that uses: OPQ
describes a project that uses: mctoolbox
MaRDI profile type: Publication
full work available at URL: s11075-009-9325-9
OpenAlex ID: W2131272303
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DOI: 10.1007/S11075-009-9325-9
description: scientific article; zbMATH DE number 5709204