A structural diagnosis of some IC orderings

We present a novel analysis of the potential effectiveness of a matrix orde ring for the incomplete Cholesky factorization ( IC) in terms of just the s parsity structure. By looking at the structure of the approximate inverse i mplicitly created by IC we can help to explain the success of reverse Cuthi ll-McKee orderings, the problems IC(0) has under red-black orderings that d isappear when extra fill is included, and where fill must be added to make fill-reducing orderings such as minimum degree effective.