Parallel nonlinear AOR method and its convergence
type: Item
instance of: scholarly article
title: Parallel nonlinear AOR method and its convergence
zbMATH Open document ID: 0859.65050
DOI: 10.1016/0898-1221(95)00190-5
publication date: 1996-07-08T00:00:00Z
review text: The paper investigates convergence of parallel nonlinear accelerated overrelaxation (AOR) methods for the solution of large scale systems of nonlinear algebraic equations in the form \(Ax+\varphi(x)=b\), where \(x,b\in \mathbb{R}^n\), \(A\) is a nonsingular matrix and \(\varphi:\mathbb{R}^n\to\mathbb{R}^n\) is a continuous diagonal nonlinear mapping. The AOR method is constructed via a multisplitting of the matrix \(A\). Under the assumptions that \(A\) is an H-matrix and \(\varphi\) satisfies certain monotonicity condition, the global convergence of the above method is proved. For \(A\) being an A-matrix some further result about monotone convergence of the method is established.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 878519
zbMATH Keywords: parallel computation
zbMATH Keywords: parallel nonlinear accelerated overrelaxation methods
zbMATH Keywords: large scale systems of nonlinear algebraic equations
zbMATH Keywords: AOR method
zbMATH Keywords: multisplitting
zbMATH Keywords: \(H\)-matrix
zbMATH Keywords: global convergence
zbMATH Keywords: \(A\)-matrix
zbMATH Keywords: monotone convergence
author: Zhong-Zhi Bai
reviewed by: R. Blaheta
MaRDI profile type: Publication
full work available at URL: 0898-1221(95)00190-5
OpenAlex ID: W2026118979
cites work: Parallel Algorithms for Nonlinear Problems
cites work: Q5652137
cites work: Multi-Splittings of Matrices and Parallel Solution of Linear Systems
cites work: On the convergence of the parallel multisplitting AOR algorithm
cites work: Convergence of relaxed parallel multisplitting methods
cites work: Regular splittings and monotone iteration functions
cites work: Convergence of parallel multisplitting iterative methods for M-matrices
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 878519