Abstract
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.
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