A unified framework for the construction of various matrix multisplitting iterative methods for large sparse system of linear equations
type: Item
instance of: scholarly article
title: A unified framework for the construction of various matrix multisplitting iterative methods for large sparse system of linear equations
zbMATH Open document ID: 0870.65025
DOI: 10.1016/S0898-1221(96)00207-6
author: Jiachang Sun
author: Deren Wang
author: Zhong-Zhi Bai
publication date: 1997-09-02T00:00:00Z
review text: From the authors' abstract and introduction: We set up a unified framework for the construction of various asynchronous parallel matrix multisplitting iterative methods for solving the large sparse system of linear equations, suitable to the SIMD and MIMD multiprocessor systems, respectively. Following suitable constructions of the linear operators, proper choices of the weighting matrices and reasonable constraints of the delayed information involved in this framework, not only all the known synchronous parallel matrix multisplitting iterative methods, can be recovered, and also a series of efficient new ones can be yielded. Hence, this framework has great generality and summarization. On the other hand, this framework itself is also an improved and generalized asynchronous parallel matrix multisplitting iterative method for the system of linear equations. Since the mutual wait, as well as the frequent communication among the processors of the MIMD multiprocessor system, are avoided in the implementation of this method, it can do useful numerical computations. This hence, makes this new method able to attain considerably high parallel computational efficiency in practical applications. Under rather weak conditions, we establish general criteria for determining the convergence, as well as the divergence, of this new framework. At last, we show how the known matrix multisplitting methods can be classified in this new framework, and what novel ones can be yielded by it, too.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 1002358
zbMATH Keywords: relaxation method
zbMATH Keywords: parallel matrix multisplitting iterative methods
zbMATH Keywords: large sparse system
zbMATH Keywords: convergence
zbMATH Keywords: divergence
MaRDI profile type: Publication
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full work available at URL: s0898-1221(96)00207-6
OpenAlex ID: W2018561210
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1002358