Volume 40, pp. 381-406, 2013.

Parallelism and robustness in GMRES with a Newton basis and deflated restarting

Desire Nuentsa Wakam and Jocelyne Erhel


The GMRES iterative method is widely used as a Krylov subspace technique for solving sparse linear systems when the coefficient matrix is nonsymmetric and indefinite. The Newton basis implementation has been proposed on distributed memory computers as an alternative to the classical approach with the Arnoldi process. The aim of our work here is to introduce a modification based on deflation techniques. This approach builds an augmented subspace in an adaptive way to accelerate the convergence of the restarted formulation. In our numerical experiments, we show the benefits of using this implementation with hybrid direct/iterative methods to solve large linear systems.

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Key words

augmented Krylov subspaces, adaptive deflated GMRES, Newton basis, hybrid linear solvers

AMS subject classifications

65F10, 65F15, 65F22

Links to the cited ETNA articles

[19]Vol. 3 (1995), pp. 160-176 Jocelyne Erhel: A parallel GMRES version for general sparse matrices
[44]Vol. 37 (2010), pp. 202-213 Valeria Simoncini: On a non-stagnation condition for GMRES and application to saddle point matrices

ETNA articles which cite this article

Vol. 43 (2014-2015), pp. 125-141 Erin Carson, Nicholas Knight, and James Demmel: An efficient deflation technique for the communication-avoiding conjugate gradient method
Vol. 47 (2017), pp. 206-230 David Imberti and Jocelyne Erhel: Varying the s in your s-step GMRES

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