We analyze the standard multigrid method accelerated by a minimal residual smoothing (MRS) technique. We show that MRS can accelerate the convergence of the slow residual components, thus accelerates the overall multigrid convergence. We prove that, under certain hypotheses, MRS stabilizes the divergence of certain slow residual components and thus stabilizes the divergent multigrid iteration. The analysis is customarily conducted on the two-level method.
1991 AMS subject classifications: 65F10, 65N06.