About Henrici's transformation for accelerating vector sequences
type: Item
instance of: scholarly article
title: About Henrici's transformation for accelerating vector sequences
zbMATH Open document ID: 0686.65001
DOI: 10.1016/0377-0427(90)90199-A
author: Hassane Sadok
published in: Journal of Computational and Applied Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The paper is concerned with a transformation of a sequence s(n) \((n=0,1,...)\) of vectors in \({\mathbb{C}}^ p\) (p\(\geq 1)\). The transformation has the form \(h(n)=s(n)-\Omega (1,n)\Omega (2,n)^{-1}\Delta s(n)\) where \(\Delta s(n)=s(n+1)-s(n),\) \(\Omega\) (1,n) is the \(p\times p\) matrix whose \((\nu +1)th\) column is \(\Delta s(n+\nu)\) \((0\leq \nu <p)\) and \(\Omega\) (2,n) is formed from \(\Delta s(n+\nu +1)-\Delta s(n+\nu)\) in the same way. The following exemplifies the results obtained. Let s(n) converge to s and satisfy the condition \(s(n+1)-s=\{B+B(n)\}\{s(n)-s\}\) where, for the spectral radius \(\rho\) (B) of B, \(\rho (B)<1\), and \(\lim B(n)=0\quad (n\to \infty).\) Let \(\det \Omega (1,n)\geq c\Pi \| \Delta s(n+\nu)\| \quad (0\leq \nu <p)\) for all \(n>N\) for some \(N\geq 0\) and \(c>0\), where \(\| \cdot \|\) denotes the Euclidean norm. Then \(\lim \| h(n)- s\| /\| s(n)-s\| =0\quad (n\to \infty).\)
Mathematics Subject Classification ID: 65B05
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4124876
zbMATH Keywords: H algorithm
zbMATH Keywords: Henrici's transformation
zbMATH Keywords: vector sequences
zbMATH Keywords: sequence transformation
zbMATH Keywords: convergence acceleration
reviewed by: Peter Wynn
MaRDI profile type: Publication
cites work: Généralisations de la transformation de Shanks, de la table de Padé et de l'\(\varepsilon\)-algorithme
cites work: Accélération de la convergence en analyse numérique
cites work: Other manifestations of the Schur complement
cites work: Some vector sequence transformations with applications to systems of equations
cites work: Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
cites work: Q5528098
cites work: Q5652137
cites work: Q4060241
cites work: Acceleration Techniques for Iterated Vector and Matrix Problems
full work available at URL: 0377-0427(90)90199-a
OpenAlex ID: W2058546081
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description: scientific article; zbMATH DE number 4124876