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Full Record Details
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
Contributors
M Arioli (STFC Rutherford Appleton Lab.)
,
D Ruiz (ENSEEHIT)
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
Funding Information
Related Research Object(s):
Licence Information:
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
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