NDLI: Exploiting Multilevel Preconditioning Techniques in Eigenvalue Computations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Sleijpen, Gerard L. G. Wubs, Fred W.
Copyright Year	2003
Abstract	In the Davidson method, any preconditioner can be exploited for the iterative computation of eigenpairs. However, the convergence of the eigenproblem solver may be poor for a high quality preconditioner. Theoretically, this counter-intuitive phenomenon with the Davidson method is remedied by the Jacobi--Davidson approach, where the preconditioned system is restricted to appropriate subspaces of codimension one. However, it is not clear how the restricted system can be solved accurately and efficiently in the case of a good preconditioner. The obvious approach introduces instabilities that hamper convergence.In this paper, we show how incomplete decomposition based on multilevel approaches can be used in a stable way. We also show how these preconditioners can be efficiently improved when better approximations for the eigenvalue of interest become available. The additional costs for updating the preconditioners are negligible. Furthermore, our approach leads to a good initial guess for the wanted eigenpair and to high quality preconditioners for nearby eigenvalues. We illustrate our ideas for the MRILU preconditioner.
Starting Page	1249
Ending Page	1272
Page Count	24
File Format	PDF
ISSN	10648275
DOI	10.1137/S1064827599361059
e-ISSN	10957197
Issue Number	4
Volume Number	25
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2004-01-01
Access Restriction	Subscribed
Subject Keyword	Davidson method eigenvalues and eigenvectors Eigenvalue problems Jacobi--Davidson multilevel ILU\--pre\-conditioners Eigenvalues, eigenvectors
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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