Some theoretical estimates of the convergence rate in multigrid methods

In this paper the theoretical estimates of convergence rates in multigrid methods are discussed. The theory is based on abstract algebraic assumptions, but we do not assume that the coarse-grid correction matrices satisfy a Galerkin ansatz. Therefore the estimates can also be applied to nonnested grids. Sharp estimates are developed for a small number of levels. The results prove the robustness of the semicoarsening multigrid method with zebra-line Gauss-Seidel iterations and sharp estimates for V- and W-cycles.