Approximate Schur complement reconditioners on serial and parallel computers

A class of preconditioning techniques for sparse matrices is considered, based on computing an approximation of the Schur complement of a (suitably ordered) matrix. The techniques generalize the reduced system methodology for 2-cyclic matrices to non-2-cyclic matrices, and in addition, they are well suited to parallel architectures. Their effectiveness with numerical experiments on a nine-point finite-difference operator is demonstrated, and an analysis showing that they can be implemented efficiently on multiprocessors is presented.