Existence and Conditioning Properties of Sparse Approximate Block Factorizations
Robert Beauwens, Mustapha Ben Bouzid · SIAM Journal on Numerical Analysis · 1988
A particular class of sparse approximate block $LU$ factorizations is investigated. Sufficient conditions are determined for the existence of $B = LP^{ - 1} U$ for a given coefficient matrix A. Bounds on the spectral condition number of $B^{ - 1} A$ are obtained for symmetric B and A. When applied to discrete multidimensional elliptic partial differential equations, these results lead, under reasonable assumptions, to $O(h^{ - 1} )$ spectral condition numbers.