911 research outputs found
Evaluating the Impact of SDC on the GMRES Iterative Solver
Increasing parallelism and transistor density, along with increasingly
tighter energy and peak power constraints, may force exposure of occasionally
incorrect computation or storage to application codes. Silent data corruption
(SDC) will likely be infrequent, yet one SDC suffices to make numerical
algorithms like iterative linear solvers cease progress towards the correct
answer. Thus, we focus on resilience of the iterative linear solver GMRES to a
single transient SDC. We derive inexpensive checks to detect the effects of an
SDC in GMRES that work for a more general SDC model than presuming a bit flip.
Our experiments show that when GMRES is used as the inner solver of an
inner-outer iteration, it can "run through" SDC of almost any magnitude in the
computationally intensive orthogonalization phase. That is, it gets the right
answer using faulty data without any required roll back. Those SDCs which it
cannot run through, get caught by our detection scheme
A flexible and adaptive Simpler GMRES with deflated restarting for shifted linear systems
In this paper, two efficient iterative algorithms based on the simpler GMRES
method are proposed for solving shifted linear systems. To make full use of the
shifted structure, the proposed algorithms utilizing the deflated restarting
strategy and flexible preconditioning can significantly reduce the number of
matrix-vector products and the elapsed CPU time. Numerical experiments are
reported to illustrate the performance and effectiveness of the proposed
algorithms.Comment: 17 pages. 9 Tables, 1 figure; Newly update: add some new numerical
results and correct some typos and syntax error
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