Low-rank improvements of two-level grid preconditioned matrices

As an alternative to basic two-level and multilevel iteration preconditioners for elliptic partial differential equations, it is shown that low-rank approximations, based on approximate eigenvectors to the largest eigenvalues of the inverse two-level Schur complement matrix, can give arbitrarily accurate preconditioners that hold uniformly with respect to mesh sizes. The methods are particularly efficient for problems with multiple right hand sides.