On the convergence of a class of parallel decomposition-type relaxation methods
type: Item
instance of: scholarly article
title: On the convergence of a class of parallel decomposition-type relaxation methods
zbMATH Open document ID: 0870.65026
DOI: 10.1016/0096-3003(95)00297-9
author: Yangfeng Su
author: Zhong-Zhi Bai
published in: Applied Mathematics and Computation
publication date: 1997-09-02T00:00:00Z
review text: The paper describes the development of a new class of parallel decomposition-type accelerated overrelaxation (AOR) methods, which are suitable to the SIMD-systems. Thereby, a general block form of a linear system of equations with a nonsingular matrix is considered. At first, the parallel decomposition-type Jacobi method, the parallel decomposition-type Gauss-Seidel method, and the parallel decomposition-type successive overrelaxation (SOR) method are generated by fixing the values of the two relaxation parameters that can be arbitrarily chosen in the parallel decomposition-type AOR method. Furthermore, sufficient and (or) necessary conditions for the convergence of the various schemes are presented for the cases that the coefficient matrix is an \(L\)-matrix, \(H\)-matrix, and a symmetric positive definite matrix, respectively. Finally, numerical results concerning two concrete examples are furnished to demonstrate the efficiency of the method as well as the validity of the convergence theories.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 1006539
zbMATH Keywords: numerical examples
zbMATH Keywords: accelerated overrelaxation methods
zbMATH Keywords: successive overrelaxation method
zbMATH Keywords: \(L\)-matrix
zbMATH Keywords: \(H\)-matrix
zbMATH Keywords: parallel computation
zbMATH Keywords: decomposition method
zbMATH Keywords: Jacobi method
zbMATH Keywords: Gauss-Seidel method
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: 0096-3003(95)00297-9
OpenAlex ID: W2089141442
cites work: Accelerated Overrelaxation Method
cites work: Q4718698
cites work: Q5342712
description: scientific article; zbMATH DE number 1006539