A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems

doi:10.4208/eajam.160816.131016a

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	A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems
	Miao, Cun-Qiang
	2017-02-01
发表期刊	EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
ISSN	2079-7362
卷号	7 期号:1 页码:21-37
摘要	For symmetric eigenvalue problems, we constructed a three-term recurrence polynomial filter by means of Chebyshev polynomials. The new filtering technique does not need to solve linear systems and only needs matrix-vector products. It is a memory conserving filtering technique for its three-term recurrence relation. As an application, we use this filtering strategy to the Davidson method and propose the filtered-Davidson method. Through choosing suitable shifts, this method can gain cubic convergence rate locally. Theory and numerical experiments show the efficiency of the new filtering technique.
关键词	Symmetric eigenproblem filtering technique Chebyshev polynomials Krylov subspace Davidson-type method
DOI	10.4208/eajam.160816.131016a
语种	英语
资助项目	National Natural Science Foundation for Creative Research Groups, P.R. China[11021101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000395402400002
出版者	CAMBRIDGE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25056
专题	中国科学院数学与系统科学研究院
通讯作者	Miao, Cun-Qiang
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Miao, Cun-Qiang. A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems[J]. EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,2017,7(1):21-37.
APA	Miao, Cun-Qiang.(2017).A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems.EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,7(1),21-37.
MLA	Miao, Cun-Qiang."A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems".EAST ASIAN JOURNAL ON APPLIED MATHEMATICS 7.1(2017):21-37.