Modified incomplete orthogonal factorization methods using Givens rotations

doi:10.1007/s00607-009-0065-4

	Modified incomplete orthogonal factorization methods using Givens rotations
	Bai, Zhong-Zhi; Yin, Jun-Feng
	2009-09-01
发表期刊	COMPUTING
ISSN	0010-485X
卷号	86 期号:1 页码:53-69
摘要	We present a class of new preconditioners based on the incomplete Givens orthogonalization (IGO) methods for solving large sparse systems of linear equations. In the new methods, instead of dropping entries and accepting fill-ins according to the magnitudes of values and the sparsity patterns, we adopt a diagonal compensation strategy, in which the dropped entries are re-used by adding to the main diagonal entries of the same rows of the incomplete upper-triangular factors, possibly after suitable relaxation treatments, so that certain constraints on the preconditioning matrices are further satisfied. This strategy can make the computed preconditioning matrices possess certain desired properties, e.g., having the same weighted row sums as the target matrices. Theoretical analysis shows that these modified incomplete Givens orthogonalization (MIGO) methods can preserve certain useful properties of the original matrix, and numerical results are used to verify the stability, the accuracy, and the efficiency of the MIGO methods employed to precondition the Krylov subspace iteration methods such as GMRES. Both theoretical and numerical studies show that the MIGO methods may have the potential to present high-quality preconditioners for large sparse nonsymmetric matrices.
关键词	Preconditioner Givens rotation Incomplete orthogonal factorization Nonsymmetric matrix
DOI	10.1007/s00607-009-0065-4
语种	英语
资助项目	National Basic Research Program[2005CB321702] ; China Outstanding Young Scientist Foundation[10525102] ; National Natural Science Foundation[10471146]
WOS研究方向	Computer Science
WOS类目	Computer Science, Theory & Methods
WOS记录号	WOS:000269926700004
出版者	SPRINGER WIEN
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7649
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	Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Yin, Jun-Feng. Modified incomplete orthogonal factorization methods using Givens rotations[J]. COMPUTING,2009,86(1):53-69.
APA	Bai, Zhong-Zhi,&Yin, Jun-Feng.(2009).Modified incomplete orthogonal factorization methods using Givens rotations.COMPUTING,86(1),53-69.
MLA	Bai, Zhong-Zhi,et al."Modified incomplete orthogonal factorization methods using Givens rotations".COMPUTING 86.1(2009):53-69.