EXISTENCE AND CONDITIONING PROPERTIES OF SPARSE

A particular class of sparse approximate block LU factorizations is investigated. Sufficient conditions are determined for the existence of B = LP-' U for a given coefficient matrix A. Bounds on the spectral condition number of B-'A are obtained for symmetric B and A. When applied to discrete multidimensional elliptic partial differential equations, these results lead, under reasonable assumptions, to 0(h-') spectral condition numbers.