Preconditioning by incomplete block elimination

The recursive construction of Schur-complements is used to construct a multi-level preconditioner for an iterative linear solver. For each level, the removed unknowns are selected in such a way that the eliminated matrix block is strictly diagonally dominant. A Newton-type iteration scheme is used to construct a sparse approximate inverse of this sub-matrix. The threshold for the diagonal dominance controls the computational effort to achieve a certain accuracy in the Newton iteration. We present a modification of the greedy algorithm in order to identify a suitable sub-matrix that is diagonally dominant and ensures a stable forward and backward substitution. Some examples are presented. Copyright (C) 2000 John Wiley & Sons, Ltd.