A class of incomplete orthogonal factorization methods. I: Methods and theories

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	A class of incomplete orthogonal factorization methods. I: Methods and theories
	Bai, ZZ ; Duff, IS ; Wathen, AJ
	2001
发表期刊	BIT
ISSN	0006-3835
卷号	41 期号:1 页码:53-70
摘要	We present a class of incomplete orthogonal factorization methods based on Givens rotations for large sparse unsymmetric matrices. These methods include: Incomplete Givens Orthogonalization (IGO-method) and its generalisation (GIGO-method), which drop entries from the incomplete orthogonal and upper triangular factors by position; Threshold Incomplete Givens Orthogonalization (TIGO(tau)-method), which drops entries dynamically by their magnitudes; and its generalisation (GTIGO(tau; p)-method), which drops entries dynamically by both their magnitudes and positions. Theoretical analyses show that these methods can produce a nonsingular sparse incomplete upper triangular factor and either a complete orthogonal factor or a sparse nonsingular incomplete orthogonal factor for a general nonsingular matrix. Therefore, these methods can potentially generate efficient preconditioners for Krylov subspace methods for solving large sparse systems of linear equations. Moreover, the upper triangular factor is an incomplete Cholesky factorization preconditioner for the normal equations matrix from least-squares problems.
关键词	preconditioning linear systems sparse least squares modified Gram-Schmidt orthogonalization Givens rotations incomplete orthogonal factorizations
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:000167334800003
出版者	SWETS ZEITLINGER PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/15878
专题	中国科学院数学与系统科学研究院
作者单位	1.Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China 2.Rutherford Appleton Lab, Atlas Ctr, Chilton OX11 0QD, Oxon, England 3.Univ Oxford, Comp Lab, Oxford OX1 3QD, England
推荐引用方式 GB/T 7714	Bai, ZZ,Duff, IS,Wathen, AJ. A class of incomplete orthogonal factorization methods. I: Methods and theories[J]. BIT,2001,41(1):53-70.
APA	Bai, ZZ,Duff, IS,&Wathen, AJ.(2001).A class of incomplete orthogonal factorization methods. I: Methods and theories.BIT,41(1),53-70.
MLA	Bai, ZZ,et al."A class of incomplete orthogonal factorization methods. I: Methods and theories".BIT 41.1(2001):53-70.