The Weighted Distributed Modification ILU Factorisation

Victor Eijkhout

Department of Computer Science, 107 Ayres Hall, University of Tennessee, Knoxville TN 37996


Abstract

The quest for the ultimate incomplete factorisation is a struggle between the demand for accuracy, and the demand for the well-definedness of the factorisation. It is a well known phenomenon that ordinary ILU can break down, even on SPD matrices. Various strategies to guarantee a well-defined factorisation exist, but they often reduce the accuracy of the factorisation. I will present a new factorisation that has strong guarantees for its existence, and exhibits a reasonable robustness in practical tests. The main idea behind this factorisation is that fill-in in (i,j) is scaled, and moved to both the (i,j) and (j,j) diagonal elements.