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DOI 10.5286/raltr.2009014
Persistent URL http://purl.org/net/epubs/work/53477
Record Status Checked
Record Id 53477
Title Flexible deflation in Krylov methods with Chebyshev-based polynomial filters
Abstract We consider the solution of ill-conditioned symmetric and positive definite large sparse linear systems of equations. These arise, for instance, when using some symmetrizing pre- conditioning technique for solving a general (possibly unsymmetric) ill-conditioned linear system, or in domain decomposition of a numerically dfficult elliptic problem. Combining Chebyshev iterations with the Lanczos algorithm, we propose a way to identify and extract precise information related to the ill-conditioned part of the given linear system. This approach is equivalent to a flexible deflation based on Chebyshev filters. The potential of this combination, which can be related to the factorization and direct solution of linear systems, is illustrated numerically and theoretically. In particular, we also present a general theory that relates the level of filtering to the accuracy of the computed solution.
Organisation CSE , CSE-NAG , STFC
Keywords Lanczos method , Engineering , Chebyshev polynomial Filtering
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2009-014. STFC, 2009. arruLAA-2009-14.pdf 2009