Geodesic
Parallelism and robustness in GMRES with a Newton basis and deflated restarting
Electronic transactions on numerical analysis, Tome 40 (2013), pp. 381-406
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.
Classification : 65F10, 65F15, 65F22
Keywords: augmented Krylov subspaces, adaptive deflated GMRES, Newton basis, hybrid linear solvers 
@article{ETNA_2013__40__a5,
     author = {Wakam,  Desire Nuentsa and Erhel,  Jocelyne},
     title = {Parallelism and robustness in {GMRES} with a {Newton} basis and deflated restarting},
     journal = {Electronic transactions on numerical analysis},
     pages = {381--406},
     year = {2013},
     volume = {40},
     zbl = {1288.65042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2013__40__a5/}
}
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%A Erhel,  Jocelyne
%T Parallelism and robustness in GMRES with a Newton basis and deflated restarting
%J Electronic transactions on numerical analysis
%D 2013
%P 381-406
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%F ETNA_2013__40__a5
Wakam,  Desire Nuentsa; Erhel,  Jocelyne. Parallelism and robustness in GMRES with a Newton basis and deflated restarting. Electronic transactions on numerical analysis, Tome 40 (2013), pp. 381-406. http://geodesic.mathdoc.fr/item/ETNA_2013__40__a5/