On the convergence of asynchronous iteration methods for nonlinear paracontractions and consistent linear systems
type: Item
instance of: scholarly article
title: On the convergence of asynchronous iteration methods for nonlinear paracontractions and consistent linear systems
zbMATH Open document ID: 0936.65026
DOI: 10.1016/S0024-3795(98)10060-5
author: Matthias Pott
published in: Linear Algebra and its Applications
publication date: 1999-11-28T00:00:00Z
review text: The concept of paracontracting operators for fixed point problems and their solution with asynchronous methods was introduced by \textit{L. Elsner, I. Koltracht} and \textit{M. Neumann}, [Numer. Math. 62, No.~3, 305-319 (1992; Zbl 0763.65035)]. The author presents an extension of their results with respect to the properties of the pool of operators from which a common fixed point is searched. As an application of the theory, asynchronous iteration methods for consistent linear systems of equations where the coefficient matrices are singular \(M\)-matrices are considered. The theory of paracontractions and confluence is used for an extension of the results obtained by \textit{B. Lubashevski} and \textit{D. Mitra} [J. Assoc. Comput. Math. 33, No.~1, 130-150 (1986; Zbl 0641.65033)] on asynchronous iteration methods for the Perron-vector problem in the reducible-affine case.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 1370996
zbMATH Keywords: asynchronous iterations
zbMATH Keywords: consistent linear systems
zbMATH Keywords: convergence
zbMATH Keywords: paracontacting operators
zbMATH Keywords: fixed point problems
zbMATH Keywords: singular \(M\)-matrices
reviewed by: Krassimir Georgiev
MaRDI profile type: Publication
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full work available at URL: s0024-3795(98)10060-5
OpenAlex ID: W2019243969
description: scientific article; zbMATH DE number 1370996