A BLOCK LANCZOS METHOD FOR THE LINEAR RESPONSE EIGENVALUE PROBLEM

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	A BLOCK LANCZOS METHOD FOR THE LINEAR RESPONSE EIGENVALUE PROBLEM
	Teng, Zhongming 1; Zhang, Lei-Hong 2
刊名	ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
	2017
卷号	46 页码:505-523
关键词	linear response eigenvalue problems block Lanczos methods convergence analysis thick-restart
ISSN号	1068-9613
英文摘要	In the linear response eigenvalue problem arising from computational quantum chemistry and physics one needs to compute a small portion of eigenvalues around zero together with the associated eigenvectors. Lanczos-type methods are particularly suitable for such a task. However, single-vector Lanczos methods can only find one copy of any multiple eigenvalue and can be very slow when the desired eigenvalues form a cluster. In this paper, we propose a block Lanczos-type implementation for the linear response eigenvalue problem, which is able to compute a cluster of eigenvalues much faster and more efficiently than the single-vector version. Convergence results are established and reveal the accuracy of the approximations of eigenvalues in a cluster and of the eigenspace. A practical thick-restart procedure is introduced to alleviate the increasing numerical difficulties of the block Lanczos method in computational costs, memory demands, and numerical stability. Numerical examples are presented to support the effectiveness of the thick-restart block Lanczos method.
WOS研究方向	Mathematics
语种	英语
出版者	KENT STATE UNIVERSITY
WOS记录号	WOS:000424522000023
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/2820]
专题	上海财经大学
通讯作者	Teng, Zhongming
作者单位	1.Fujian Agr & Forestry Univ, Coll Comp & Informat Sci, Fuzhou 350002, Fujian, Peoples R China; 2.Shanghai Univ Finance & Econ, Sch Interdisciplinary Sci, Sch Math & Res, 777 Guoding Rd, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Teng, Zhongming,Zhang, Lei-Hong. A BLOCK LANCZOS METHOD FOR THE LINEAR RESPONSE EIGENVALUE PROBLEM[J]. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS,2017,46:505-523.
APA	Teng, Zhongming,&Zhang, Lei-Hong.(2017).A BLOCK LANCZOS METHOD FOR THE LINEAR RESPONSE EIGENVALUE PROBLEM.ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS,46,505-523.
MLA	Teng, Zhongming,et al."A BLOCK LANCZOS METHOD FOR THE LINEAR RESPONSE EIGENVALUE PROBLEM".ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS 46(2017):505-523.