On the convergence of modified contractions
type: Item
instance of: scholarly article
title: On the convergence of modified contractions
zbMATH Open document ID: 0822.65045
DOI: 10.1016/0377-0427(94)90019-1
author: F. Szidarovszky
author: Ioannis Konstantinos Argyros
published in: Journal of Computational and Applied Mathematics
publication date: 1995-10-15T00:00:00Z
review text: The convergence of modified iteration methods of the form \(x_{k+ 1}= \alpha_ k{\mathbf x}_ k+ (1-\alpha_ k) A({\mathbf x}_ k)\), where \(A: D\to D\) with \(D\subseteq \mathbb{R}^ n\) being convex is studied. Earlier results, given by \textit{D. Liu} and \textit{F. Szidarovszky} [Appl. Math. Comput. 43, No. 3, 237-240 (1991; Zbl 0733.93065)], guarantee the convergence of the process (even for nonstationary cases) when the original algorithm \({\mathbf z}_{k+ 1}= A({\mathbf z}_ k)\) also converges to the unique fixed point of the mapping \(A\). In the paper, some convergence criteria, valid also in cases when the original algorithm diverges, are proved and the optimal selection of the weights \(\alpha_ k\) is determined for such cases, using the quadratic programming approach.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 758529
zbMATH Keywords: iteration methods
zbMATH Keywords: convergence
zbMATH Keywords: algorithm
zbMATH Keywords: quadratic programming
reviewed by: S.Ząbek
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90019-1
OpenAlex ID: W1987982433
cites work: Global asymptotical stability of dynamic systems with modified contractions
cites work: Q5652137
cites work: Q4016866
description: scientific article; zbMATH DE number 758529