Improving the Accuracy of GMRes with Deflated Restarting

Authors:
S. Röllin;W. Fichtner
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2007

Citing 0
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Abstract

In general, restarting the generalized minimum residual method (GMRes) slows down the convergence speed. There exist a number of methods that improve the convergence of restarted GMRes. One of them is GMRes with deflated restarting [SIAM J. Sci. Comput., 24 (2002), pp. 20-37] introduced by Morgan. This method retains a number of harmonic Ritz vectors at each restart to mitigate convergence slowdown. We investigate the accuracy of this method and propose a slight modification of it that is mathematically equivalent. We show that the new implementation has better numerical properties, especially if high accuracy of the solution is required. Numerical results are presented that confirm our theoretical results.