Convergence acceleration of some logarithmic sequences
type: Item
instance of: scholarly article
title: Convergence acceleration of some logarithmic sequences
zbMATH Open document ID: 0724.65002
DOI: 10.1016/0377-0427(90)90435-3
author: Guy Antoine Sedogbo
published in: Journal of Computational and Applied Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Let \((S_ n)\) be some real sequence defined as \((1)\quad S_{n+1}=f(S_ n)\text{ for } n\in N,\text{ where } f(x)=x+\sum_{i\geq 1}\alpha_{p+i}(x-S)^{p+i}\) with \(p\in N\), \(p\neq 0\) and \(\alpha_{p+1}<0\), \(S_ 0\) given. For \(S_ 0\) well chosen, it converges to S and \(\lim_{n\to \infty}(S_{n+1}-S)/(S_ n-S)=1\) (logarithmic convergence). The author proposes a specific study of some algorithms (modified iterated versions of Aitken's \(\Delta^ 2\) process, iterated \(\theta_ 2\)-algorithm, modified \(\epsilon\)-algorithms and \(\theta\)-algorithm) which accelerate the convergence of this type of sequences and also estimate the errors of the transformed sequences. For sequences of type (1), with \(p=1,2\), more precise results and an efficient algorithm combining the modified \(\Delta^ 2\) and \(\theta_ 2\)-algorithm are given. Finally, some numerical results are considered in order to compare the different algorithms.
Mathematics Subject Classification ID: 65B05
zbMATH DE Number: 4195007
zbMATH Keywords: error estimates
zbMATH Keywords: convergence acceleration
zbMATH Keywords: logarithmic sequences
zbMATH Keywords: epsilon algorithm
zbMATH Keywords: Aitken's delta square algorithm
zbMATH Keywords: theta algorithm
zbMATH Keywords: logarithmic convergence
zbMATH Keywords: numerical results
reviewed by: G. Dimitriu
MaRDI profile type: Publication
full work available at URL: 0377-0427(90)90435-3
OpenAlex ID: W2072292967
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description: scientific article; zbMATH DE number 4195007