The implicit application of a rational filter in the RKS method

The implicitly restarted Arnoldi method implicitly applies a polynomial filter to the Arnoldi vectors by use of orthogonal transformations. In this paper, an implicit filtering by rational functions is proposed for the rational Krylov method. This filtering is performed in an efficient way. Two appl...

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Bibliographic Details
Published in:BIT 1997-12, Vol.37 (4), p.925-947
Main Authors: De Samblanx, G., Meerbergen, K., Bultheel, A.
Format: Article
Language:English
Subjects:
Eigenvalues
Filtration
Mathematical analysis
Polynomials
Rational functions
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Summary:The implicitly restarted Arnoldi method implicitly applies a polynomial filter to the Arnoldi vectors by use of orthogonal transformations. In this paper, an implicit filtering by rational functions is proposed for the rational Krylov method. This filtering is performed in an efficient way. Two applications are considered. The first one is the filtering of unwanted eigenvalues using exact shifts. This approach is related to the use of exact shifts in the implicitly restarted Arnoldi method. Second, eigenvalue problems can have an infinite eigenvalue without physical relevance. This infinite eigenvalue can corrupt the eigensolution. An implicit filtering is proposed for avoiding such corruptions.
ISSN:0006-3835
1572-9125
DOI:10.1007/BF02510361