Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems

doi:10.1016/j.cam.2005.03.044

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems
	Bai, ZZ; Wang, ZQ
刊名	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
	2006-03-15
卷号	187 期号:2 页码:202-226
关键词	linear system block two-by-two matrix symmetric positive definite matrix restrictive preconditioner conjugate gradient method
ISSN号	0377-0427
DOI	10.1016/j.cam.2005.03.044
英文摘要	The restrictively preconditioned conjugate gradient (RPCG) method for solving large sparse system of linear equations of a symmetric positive definite and block two-by-two coefficient matrix is further studied. In fact, this RPCG method is essentially the classical preconditioned conjugate gradient (PCG) method with a specially structured preconditioner. Within this setting, we present algorithmic descriptions of two restrictive preconditioners that, respectively, employ the block Jacobi and the block symmetric Gauss-Seidel matrix splitting matrices as approximations to certain matrices involved in them, and give convergence analyses of the correspondingly induced two PCG methods. Numerical results show that these restrictive preconditioners can lead to practical and effective PCG methods for solving large sparse systems of linear equations of symmetric positive definite and block two-by-two coefficient matrices. (c) 2005 Elsevier B.V. All rights reserved.
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER SCIENCE BV
WOS记录号	WOS:000233952800005
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/3656]
专题	计算数学与科学工程计算研究所
通讯作者	Bai, ZZ
作者单位	Chinese Acad Sci, State Key Lab Sci, Inst Computat Math & Sci Engn, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Bai, ZZ,Wang, ZQ. Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2006,187(2):202-226.
APA	Bai, ZZ,&Wang, ZQ.(2006).Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,187(2),202-226.
MLA	Bai, ZZ,et al."Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 187.2(2006):202-226.