Abstract
We consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. These methods are expected to have considerable potential for resiliency to faults when implemented on massively parallel machines. We establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.
Original language | English |
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Article number | e2088 |
Journal | Numerical Linear Algebra with Applications |
Volume | 24 |
Issue number | 3 |
DOIs | |
State | Published - May 1 2017 |
Funding
This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. We would also like to thank Miroslav Tåma for providing the AINV code used in some of the numerical experiments. This study was supported by the Department of Energy (Office of Science)ERKJ247.
Funders | Funder number |
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United States Government | |
U.S. Department of Energy | |
Office of Science | ERKJ247 |
Keywords
- Monte Carlo methods
- Richardson iteration
- iterative methods
- preconditioning
- resilience
- sparse approximate inverses
- sparse linear systems