ON THE NUMERICAL BEHAVIOR OF MATRIX SPLITTING ITERATION METHODS FOR SOLVING LINEAR SYSTEMS | |
Bai, Zhong-Zhi1![]() | |
刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
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2015 | |
卷号 | 53期号:4页码:1716-1737 |
关键词 | matrix splitting stationary iteration method backward error rounding error analysis |
ISSN号 | 0036-1429 |
DOI | 10.1137/140987936 |
英文摘要 | 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. |
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 |
语种 | 英语 |
出版者 | SIAM PUBLICATIONS |
WOS记录号 | WOS:000360692100004 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/20735] ![]() |
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. |
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