On Solving Ill-Conditioned Linear Systems
  This paper presents the first results to combine two theoretically sound methods (spectral projection and multigrid methods) together to attack ill-conditioned linear systems. Our preliminary results show that the proposed algorithm applied to a Krylov subspace method takes much fewer iterations for solving an ill-conditioned problem downloaded from a popular online sparse matrix collection. 
Craig C. Douglas and Long Lee and Man-Chung Yeung
math.NA