An asynchronous parallel algorithm for solving a class of nonlinear simultaneous equations
type: Item
instance of: scholarly article
title: An asynchronous parallel algorithm for solving a class of nonlinear simultaneous equations
zbMATH Open document ID: 0729.65034
DOI: 10.1016/S0167-8191(05)80103-6
author: D. J. Evans
author: Deren Wang
published in: Parallel Computing
publication date: 1991-01-01T00:00:00Z
review text: The system of nonlinear algebraic equations \(Ax+\phi (x)=0,\) where A is an \(n\times n\) M-matrix and \(\phi\) is a diagonal isotone continuous mapping, is treated with parallel asynchronous algorithms, namely, Schwarz-alternating procedure inspired versions of Jacobi and relaxation schemes. Convergence rates are shown to be at least linear. Further, some numerical results are exhibited that were obtained through application of the developed method to a nonlinear elliptic equation discretized with finite differences, which thus amounts to a domain decomposition technique.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N22
zbMATH DE Number: 4205878
zbMATH Keywords: system of nonlinear algebraic equations
zbMATH Keywords: diagonal isotone continuous mapping
zbMATH Keywords: parallel asynchronous algorithms
zbMATH Keywords: Schwarz-alternating procedure
zbMATH Keywords: relaxation schemes
zbMATH Keywords: Convergence rates
zbMATH Keywords: numerical results
zbMATH Keywords: nonlinear elliptic equation
zbMATH Keywords: finite differences
zbMATH Keywords: domain decomposition
MaRDI profile type: Publication
full work available at URL: s0167-8191(05)80103-6
OpenAlex ID: W2000212348
description: scientific article; zbMATH DE number 4205878