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Volume 7, Issue 1
A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems

Cun-Qiang Miao

DOI: 10.4208/eajam.160816.131016a

East Asian J. Appl. Math., 7 (2017), pp. 21-37.

Published online: 2018-02

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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 eigenproblem, filtering technique, Chebyshev polynomials, Krylov subspace, Davidson-type method.

  • AMS Subject Headings

15A18, 65F15, 65F50, 34L15, 65N25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-21, author = {Cun-Qiang Miao}, title = {A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {1}, pages = {21--37}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.160816.131016a}, url = {http://global-sci.org/intro/article_detail/eajam/10732.html} }
TY - JOUR T1 - A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems AU - Cun-Qiang Miao JO - East Asian Journal on Applied Mathematics VL - 1 SP - 21 EP - 37 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.160816.131016a UR - https://global-sci.org/intro/article_detail/eajam/10732.html KW - Symmetric eigenproblem, filtering technique, Chebyshev polynomials, Krylov subspace, Davidson-type method. AB -

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.

Cun-Qiang Miao. (2018). A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems. East Asian Journal on Applied Mathematics. 7 (1). 21-37. doi:10.4208/eajam.160816.131016a
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