Analysis of a recursive 5-point/9-point factorization method

Nested recursive two-level factorization methods for nine-point difference matrices are analyzed. Somewhat similar in construction to multilevel methods for finite element matrices, these methods use recursive red-black orderings of the meshes, approximating the nine-point stencils by five-point ones in the red points and then forming the reduced system explicitly. As this Schur complement is again a nine-point matrix (on a skew grid this time), the process of approximating and factorizing can be applied anew.