Preconditioning by incomplete block elimination

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