A shift strategy for the generalized method of minimal residuals

An approach to solution of large sparse linear systems of equations is proposed. This approach is a variant of popular generalized method of minimal residuals GMRES and based on alternate correction stages and explicit restarts. The subspace for correction is constructed partly from basis vectors of Krylov subspace. A rule for selection of the desired vectors is an investigated shift strategy. The numerical experiments for linear systems, that appear as a result of stabilized finite-element approximations of convection-diffusion problems on structured and unstructured grids, are represented.