On coarse grid correction methods in Krylov subspaces

Two approaches using coarse grid correction in the course of a certain Krylov iterative process are presented. The aim of the correction is to accelerate the iterations. These approaches are based on an approximation of the function sought for by simple basis functions having finite supports. Additional acceleration can be achieved if one applies restarts of the iterative process together with the approximate solution refinement approach. In this case, the resulting process turns out to be a two-level preconditioned method. A series of numerical experiments has been carried out to show the influence of different parameters of the iterative process on the convergence.