Istituto di Matematica Applicata e Tecnologie Informatiche     
Simoncini V. A new variant of restarted GMRES. Preprint ercim.cnr.ian//1997-1050, 1997.
GMRES is an attractive iterative method for solving large non-symmetric algebraic linear systems. Computational and storage constraints usually require to restart the method after a fixed (small) number of iterations with subsequent loss of monotonic convergence properties. Trouble may be caused by the presence of eigenvalues close to the origin which are not well detected by early restarts. Unlike recent techniques that propose to include this information in later restarts, we use a new formulation of GMRES to derive a simple variant of the algorithm. The method attemps to mitigate stagnation by exploiting the smoothness of a certain polynomial near the origin, resorting to the usual method once convergence becomes truly monotonic.
Subject Linear systems, Iterative methods, Restarts, Residual polynomials

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