Sparse matrix approximations for multigrid methods

We discuss the application of sparse matrix approximations for two-grid and V-cycle multigrid methods. Sparse approximate inverses can be used as smoothers, further the Galerkin coarse matrix can be sparsified by sparse approximation techniques. Also the projection can be defined by combining sparse approximation with side conditions related to high frequency components. Numerical results are given, which demonstrate the efficiency and accuracy of the proposed strategies.