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

doi:10.1016/j.cam.2005.03.044

	Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems
	Bai, ZZ; Wang, ZQ
	2006-03-15
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	187 期号:2 页码:202-226
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.
关键词	linear system block two-by-two matrix symmetric positive definite matrix restrictive preconditioner conjugate gradient method
DOI	10.1016/j.cam.2005.03.044
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000233952800005
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3657
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.