The stable computation of formal orthogonal polynomials
type: Item
instance of: scholarly article
title: The stable computation of formal orthogonal polynomials
zbMATH Open document ID: 0848.65007
DOI: 10.1007/BF02142485
author: Bernhard Beckermann
published in: Numerical Algorithms
publication date: 1996-11-03T00:00:00Z
review text: The author presents a new variant of the Cabay-Meleshko algorithm for numerically computing pairs of basis polynomials, where the numerical orthogonality is explicitly monitored with the help of stability parameters. A corresponding error analysis is given. It is shown in one theorem, that by controlling the stability parameters, the author is able to monitor the size of the residual. The given new explicit bounds for the residuals enable finally to propose a reliable dynamical strategy for choosing the step size in the look-ahead process. The stability parameter is shown to reflect the condition number of the underlying Hankel matrix of moments. This enables to prove the weak and strong stability of the method, provided that the corresponding Hankel matrix is well conditioned.
reviewed by: R. S. Dahiya
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 65T40
zbMATH DE Number: 871271
zbMATH Keywords: formal orthogonal polynomials
zbMATH Keywords: Cabay-Meleshko algorithm
zbMATH Keywords: pairs of basis polynomials
zbMATH Keywords: stability parameters
zbMATH Keywords: error analysis
zbMATH Keywords: condition number
zbMATH Keywords: Hankel matrix of moments
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02142485
OpenAlex ID: W2045680067
description: scientific article; zbMATH DE number 871271