Geodesic
On a non-stagnation condition for GMRES and application to saddle point matrices
Electronic transactions on numerical analysis, Tome 37 (2010), pp. 202-213
In Simoncini and Szyld [Numer. Math., 109 (2008), pp. 477-487] a new non-stagnation condition for the convergence of GMRES on indefinite problems was proposed. In this paper we derive an enhanced strategy leading to a more general non-stagnation condition. Moreover, we show that the analysis also provides a good setting to derive asymptotic convergence rate estimates for indefinite problems. The analysis is then explored in the context of saddle point matrices, when these are preconditioned in a way so as to lead to nonsymmetric and indefinite systems. Our results indicate that these matrices may represent an insightful training set towards the understanding of the interaction between indefiniteness and stagnation.
Classification : 65F10, 65N22, 65F50
Keywords: saddle point matrices, large linear systems, GMRES, stagnation 
@article{ETNA_2010__37__a13,
     author = {Simoncini,  Valeria},
     title = {On a non-stagnation condition for {GMRES} and application to saddle point matrices},
     journal = {Electronic transactions on numerical analysis},
     pages = {202--213},
     year = {2010},
     volume = {37},
     zbl = {1206.65136},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2010__37__a13/}
}
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Simoncini,  Valeria. On a non-stagnation condition for GMRES and application to saddle point matrices. Electronic transactions on numerical analysis, Tome 37 (2010), pp. 202-213. http://geodesic.mathdoc.fr/item/ETNA_2010__37__a13/