THE JOINT BIDIAGONALIZATION OF A MATRIX PAIR WITH INACCURATE INNER ITERATIONS

doi:10.1137/22M1541083

	THE JOINT BIDIAGONALIZATION OF A MATRIX PAIR WITH INACCURATE INNER ITERATIONS
	Li, Haibo 1,2
	2024
发表期刊	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN	0895-4798
卷号	45 期号:1 页码:232-259
摘要	The joint bidiagonalization (JBD) process iteratively reduces a matrix pair {A, L\} to two bidiagonal forms simultaneously, which can be used for computing a partial generalized singular value decomposition (GSVD) of {A, L\} . The process has a nested inner-outer iteration structure, where the inner iteration usually cannot be computed exactly. In this paper, we study the inaccurately computed inner iterations of JBD by first investigating the influence of computational error of the inner iteration on the outer iteration, and then proposing a reorthogonalized JBD (rJBD) process to keep orthogonality of a part of Lanczos vectors. An error analysis of the rJBD is carried out to build up connections with Lanczos bidiagonalizations. The results are then used to investigate convergence and accuracy of the rJBD based GSVD computation. It is shown that the accuracy of computed GSVD components depends on the computing accuracy of inner iterations and the condition number of (AT, LT )T , while the convergence rate is not affected very much. For practical JBD based GSVD computations, our results can provide a guideline for choosing a proper computing accuracy of inner iterations in order to obtain approximate GSVD components with a desired accuracy. Numerical experiments are made to confirm our theoretical results.
关键词	joint bidiagonalization GSVD inner iteration stopping tolerance Lanczos bidiag- onalization convergence and accuracy
DOI	10.1137/22M1541083
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[3192270206]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:001171693500005
出版者	SIAM PUBLICATIONS
引用统计	被引频次：1[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/38705
专题	中国科学院计算技术研究所期刊论文_英文
通讯作者	Li, Haibo
作者单位	1.Huawei Technol, Comp Syst Optimizat Lab, Beijing 100094, Peoples R China 2.Chinese Acad Sci, Inst Comp Technol, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Haibo. THE JOINT BIDIAGONALIZATION OF A MATRIX PAIR WITH INACCURATE INNER ITERATIONS[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2024,45(1):232-259.
APA	Li, Haibo.(2024).THE JOINT BIDIAGONALIZATION OF A MATRIX PAIR WITH INACCURATE INNER ITERATIONS.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,45(1),232-259.
MLA	Li, Haibo."THE JOINT BIDIAGONALIZATION OF A MATRIX PAIR WITH INACCURATE INNER ITERATIONS".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 45.1(2024):232-259.