Multipreconditioned Gmres for Shifted Systems
Abstract
An implementation of GMRES with multiple preconditioners is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring the matrix-vector product with the shifted matrix. Furthermore, the multipreconditioned search space is shown to grow only linearly with the number of preconditioners. This allows for a more efficient implementation of the algorithm. The proposed implementation is tested on shifted systems that arise in computational hydrology and the evaluation of different matrix functions. The numerical results indicate the effectiveness of the proposed approach.
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Information & Authors
Information
Published In
SIAM Journal on Scientific Computing
Pages: S222 - S247
DOI: 10.1137/16M1068694
ISSN (online): 1095-7197
Copyright
© 2017, Society for Industrial and Applied Mathematics.
History
Submitted: 1 April 2016
Accepted: 19 January 2017
Published online: 26 October 2017
Keywords
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Authors
Funding Information
National Science Foundation https://doi.org/10.13039/100000001 : DMS-1418882
U.S. Department of Energy https://doi.org/10.13039/100000015 : DE-SC0016578
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