CONSTRAINT PRECONDITIONERS FOR SYMMETRIC INDEFINITE MATRICES

doi:10.1137/080720243

	CONSTRAINT PRECONDITIONERS FOR SYMMETRIC INDEFINITE MATRICES
	Bai, Zhong-Zhi1 ; Ng, Michael K.2; Wang, Zeng-Qi 3
	2009
发表期刊	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN	0895-4798
卷号	31 期号:2 页码:410-433
摘要	We study the eigenvalue bounds of block two-by-two nonsingular and symmetric indeifnite matrices whose (1, 1) block is symmetric positive definite and Schur complement with respect to its (2, 2) block is symmetric indefinite. A constraint preconditioner for this matrix is constructed by simply replacing the (1, 1) block by a symmetric and positive definite approximation, and the spectral properties of the preconditioned matrix are discussed. Numerical results show that, for a suitably chosen (1, 1) block-matrix, this constraint preconditioner outperforms the block-diagonal and the block-tridiagonal ones in iteration step and computing time when they are used to accelerate the GMRES method for solving these block two-by-two symmetric positive indefinite linear systems. The new results extend the existing ones about block two-by-two matrices of symmetric negative semidefinite (2, 2) blocks to those of general symmetric (2, 2) blocks.
关键词	symmetric indefinite systems constraint preconditioners
DOI	10.1137/080720243
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000267745500011
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/7208
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, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China 2.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China 3.Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Ng, Michael K.,Wang, Zeng-Qi. CONSTRAINT PRECONDITIONERS FOR SYMMETRIC INDEFINITE MATRICES[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2009,31(2):410-433.
APA	Bai, Zhong-Zhi,Ng, Michael K.,&Wang, Zeng-Qi.(2009).CONSTRAINT PRECONDITIONERS FOR SYMMETRIC INDEFINITE MATRICES.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,31(2),410-433.
MLA	Bai, Zhong-Zhi,et al."CONSTRAINT PRECONDITIONERS FOR SYMMETRIC INDEFINITE MATRICES".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 31.2(2009):410-433.