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A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems
Miao, Cun-Qiang
2017-02-01
Source PublicationEAST ASIAN JOURNAL ON APPLIED MATHEMATICS
ISSN2079-7362
Volume7Issue:1Pages:21-37
AbstractFor 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.
KeywordSymmetric eigenproblem filtering technique Chebyshev polynomials Krylov subspace Davidson-type method
DOI10.4208/eajam.160816.131016a
Language英语
Funding ProjectNational Natural Science Foundation for Creative Research Groups, P.R. China[11021101]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000395402400002
PublisherCAMBRIDGE UNIV PRESS
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25056
Collection中国科学院数学与系统科学研究院
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
Recommended Citation
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.
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