ON THE NUMERICAL BEHAVIOR OF MATRIX SPLITTING ITERATION METHODS FOR SOLVING LINEAR SYSTEMS

doi:10.1137/140987936

	ON THE NUMERICAL BEHAVIOR OF MATRIX SPLITTING ITERATION METHODS FOR SOLVING LINEAR SYSTEMS
	Bai, Zhong-Zhi1 ; Rozloznik, Miroslav 2
	2015
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	53 期号:4 页码:1716-1737
摘要	We study the numerical behavior of stationary one-step or two-step matrix splitting iteration methods for solving large sparse systems of linear equations. We show that inexact solutions of inner linear systems associated with the matrix splittings may considerably influence the accuracy of the approximate solutions computed in finite precision arithmetic. For a general stationary matrix splitting iteration method, we analyze two mathematically equivalent implementations and discuss the conditions when they are componentwise or normwise forward or backward stable. We distinguish two different forms of matrix splitting iteration methods and prove that one of them is significantly more accurate than the other when employing inexact inner solves. The theoretical results are illustrated by numerical experiments with an inexact one-step and an inexact two-step splitting iteration method.
关键词	matrix splitting stationary iteration method backward error rounding error analysis
DOI	10.1137/140987936
语种	英语
资助项目	National Basic Research Program[2011CB309703] ; National Natural Science Foundation[91118001] ; National Natural Science Foundation for Creative Research Groups[11321061] ; Defense Industrial Technology Development Program, People's Republic of China[B1520133016] ; Grant Agency of the Czech Republic[13-06684S]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000360692100004
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20736
专题	计算数学与科学工程计算研究所
通讯作者	Bai, Zhong-Zhi
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100190, Peoples R China 2.Acad Sci Czech Republic, Inst Comp Sci, CZ-18207 Prague 8, Czech Republic
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Rozloznik, Miroslav. ON THE NUMERICAL BEHAVIOR OF MATRIX SPLITTING ITERATION METHODS FOR SOLVING LINEAR SYSTEMS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2015,53(4):1716-1737.
APA	Bai, Zhong-Zhi,&Rozloznik, Miroslav.(2015).ON THE NUMERICAL BEHAVIOR OF MATRIX SPLITTING ITERATION METHODS FOR SOLVING LINEAR SYSTEMS.SIAM JOURNAL ON NUMERICAL ANALYSIS,53(4),1716-1737.
MLA	Bai, Zhong-Zhi,et al."ON THE NUMERICAL BEHAVIOR OF MATRIX SPLITTING ITERATION METHODS FOR SOLVING LINEAR SYSTEMS".SIAM JOURNAL ON NUMERICAL ANALYSIS 53.4(2015):1716-1737.