The implicit application of a rational lter in the RKS methodGorik
نویسندگان
چکیده
The implicitly restarted Arnoldi method implicitly applies a polynomial lter to the Arnoldi vectors by use of orthogonal transformations. In this paper, an implicit ltering by rational functions is proposed for the rational Krylov method. This ltering is performed in an eecient way. Two applications are considered. The rst one is the ltering 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 innnite eigenvalue without physical relevance. This innnite eigenvalue can corrupt the eigensolution. An implicit ltering is proposed for avoiding such corruptions.
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