Further convergence and stability results for the generalized Richardson extrapolation process \(GREP^{(1)}\) with an application to the \(D^{(1)}\)-transformation for infinite integrals
type: Item
instance of: scholarly article
title: Further convergence and stability results for the generalized Richardson extrapolation process \(GREP^{(1)}\) with an application to the \(D^{(1)}\)-transformation for infinite integrals
zbMATH Open document ID: 0958.65008
DOI: 10.1016/S0377-0427(99)90226-1
author: Avram Sidi
published in: Journal of Computational and Applied Mathematics
publication date: 2001-03-28T00:00:00Z
review text: The author studies the convergence and stability properties of a generalized Richardson extrapolation process for the case \(\varphi(t) = \alpha t^{\delta}\) as \(t\to 0+\) in which \(\delta\) is complex when the set of extrapolation points is \(\{t_i=t_0\cdot \omega^i, i=0,1,\dots\}\) with \(\omega\in (0,1)\). He applies this analysis to the D1-transformation of \textit{D. Levin} and \textit{A. Sidi} [Appl. Math. Comput. 9, 175-215 (1981; Zbl 0487.65003)] that is a generalized Richarson extrapolation process. Several numerical examples are given.
Mathematics Subject Classification ID: 65B05
zbMATH DE Number: 1398811
zbMATH Keywords: Richarson extrapolation
zbMATH Keywords: convergence acceleration
zbMATH Keywords: stability
zbMATH Keywords: D1-transformation
zbMATH Keywords: numerical examples
reviewed by: Antonio López-Carmona
MaRDI profile type: Publication
cites work: Q3323133
cites work: Q5724171
cites work: Q5788558
cites work: Two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series
cites work: Q5662429
cites work: Some Properties of a Generalization of the Richardson Extrapolation Process
cites work: An algorithm for a special case of a generalization of the Richardson extrapolation process
cites work: Convergence Analysis for a Generalized Richardson Extrapolation Process with an Application to the d (1) -Transformation on Convergent and Divergent Logarithmic Sequences
description: scientific article; zbMATH DE number 1398811