Acceleration of the Method of Alternating Projections on subspaces by GMRES

In this paper we propose a GMRES-accelerated version of the Method of Alternating Projections (MAP) for subspaces. It is proved that the accelerated version not only converges to a feasible solution, but also solves a best approximation problem. Comparisons are made with other accelerations proposed in the literature, for solving saddle point problems.