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A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems

Part of: Basic linear algebra Partial differential equations, boundary value problems Ordinary differential operators Numerical linear algebra

Published online by Cambridge University Press:  31 January 2017

Cun-Qiang Miao
Cun-Qiang Miao*
Affiliation:
Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
*
*Corresponding author. Email address:miaocunqiang@lsec.cc.ac.cn (C.-Q. Miao)
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Abstract

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.

Keywords

Symmetric eigenproblemfiltering techniqueChebyshev polynomialsKrylov subspaceDavidson-type method

MSC classification

Secondary: 15A18: Eigenvalues, singular values, and eigenvectors 65F15: Eigenvalues, eigenvectors 65F50: Sparse matrices 34L15: Eigenvalues, estimation of eigenvalues, upper and lower bounds 65N25: Eigenvalue problems

Information

Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 1 , February 2017 , pp. 21 - 37
Copyright
Copyright © Global-Science Press 2017 

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