Geodesic
Some remarks on the restarted and augmented GMRES method
Electronic transactions on numerical analysis, Tome 31 (2008), pp. 221-227
Starting from the residual estimates for GMRES formulated by many authors, usually in terms of the quotient of the Hermitian part and the norm of a matrix or by using the field of values of a matrix, we present more general estimates which hold also for restarted and augmented GMRES. Sufficient conditions for convergence are formulated. All estimates are independent on the choice of an initial approximation.
Classification : 15A06, 65F10
Keywords: linear equations, restarted and augmented GMRES method, residual bounds, non-stagnation conditions 
@article{ETNA_2008__31__a9,
     author = {Z{\'\i}tko,  Jan},
     title = {Some remarks on the restarted and augmented {GMRES} method},
     journal = {Electronic transactions on numerical analysis},
     pages = {221--227},
     year = {2008},
     volume = {31},
     zbl = {1171.65024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__31__a9/}
}
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%T Some remarks on the restarted and augmented GMRES method
%J Electronic transactions on numerical analysis
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%F ETNA_2008__31__a9
Zítko,  Jan. Some remarks on the restarted and augmented GMRES method. Electronic transactions on numerical analysis, Tome 31 (2008), pp. 221-227. http://geodesic.mathdoc.fr/item/ETNA_2008__31__a9/