Year: 2017
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.160816.131016a
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 1 : pp. 21–37
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Symmetric eigenproblem filtering technique Chebyshev polynomials Krylov subspace Davidson-type method.
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