Structured preconditioners for nonsingular matrices of block two-by-two structures

	Structured preconditioners for nonsingular matrices of block two-by-two structures
	Bai, ZZ
	2006
发表期刊	MATHEMATICS OF COMPUTATION
ISSN	0025-5718
卷号	75 期号:254 页码:791-815
摘要	For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of practical and efficient structured preconditioners through matrix transformation and matrix approximations. For the specific versions such as modified block Jacobi-type, modified block Gauss-Seidel-type, and modified block unsymmetric (symmetric) Gauss-Seidel-type preconditioners, we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices. Also, we show that when these structured preconditioners are employed to precondition the Krylov subspace methods such as GMRES and restarted GMRES, fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two-by-two coefficient matrices. In particular, these structured preconditioners can lead to efficient and high-quality preconditioning matrices for some typical matrices from the real-world applications.
关键词	block two-by-two matrix preconditioner modified block relaxation iteration eigenvalue distribution positive definiteness
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000236723300014
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2489
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, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Bai, ZZ. Structured preconditioners for nonsingular matrices of block two-by-two structures[J]. MATHEMATICS OF COMPUTATION,2006,75(254):791-815.
APA	Bai, ZZ.(2006).Structured preconditioners for nonsingular matrices of block two-by-two structures.MATHEMATICS OF COMPUTATION,75(254),791-815.
MLA	Bai, ZZ."Structured preconditioners for nonsingular matrices of block two-by-two structures".MATHEMATICS OF COMPUTATION 75.254(2006):791-815.