The Mathematical Institute, University of Oxford, Eprints Archive

The Tortoise and the Hare restart GMRES

Embree, Mark (2001) The Tortoise and the Hare restart GMRES. Technical Report. Unspecified. (Submitted)



When solving large nonsymmetric systems of linear equations with the restarted GMRES algorithm, one is inclined to select a relatively large restart parameter in the hope of mimicking the full GMRES process. Surprisingly, cases exist where small values of the restart parameter yield convergence in fewer iterations than larger values. Here, two simple examples are presented where GMRES(1) converges exactly in three iterations, while GMRES(2) stagnates. One of these examples reveals that GMRES(1) convergence can be extremely sensitive to small changes in the initial residual.

Item Type:Technical Report (Technical Report)
Subjects:D - G > Dynamical systems and ergodic theory
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1229
Deposited By: Lotti Ekert
Deposited On:20 May 2011 08:20
Last Modified:29 May 2015 18:55

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