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Schwarz Methods: To Symmetrize or not to SymmetrizeA preconditioning theory for Schwarz methods is presented. The theory establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition and multigrid. This paper illustrates why symmetrizing may be a bad idea for linear methods. Numerical examples are presented for a test problem.
Document ID
19970006884
Acquisition Source
Langley Research Center
Document Type
Conference Paper
Authors
Holst, Michael
(California Inst. of Tech. Pasadena, CA United States)
Vandewalle, Stefan
(California Inst. of Tech. Pasadena, CA United States)
Date Acquired
August 17, 2013
Publication Date
September 1, 1996
Publication Information
Publication: Seventh Copper Mountain Conference on Multigrid Methods
Issue: Part 1
Subject Category
Numerical Analysis
Accession Number
97N13777
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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