Incomplete factorizations of singular linear systems

Recent works have shown that, whenA is a Stieltjes matrix, its so-called modified incomplete factorizations provide effective preconditioning matrices for solvingAx=b by polynomially accelerated iterative methods. We extend here these results to the singular case with the conclusion that the latter techniques are able to solve singular systems at the same speed as regular systems.Research supported by the Fonds National de la Recherche Scientifique (Belgium) — Aspirant.