A robust incomplete factorization preconditioner for positive definite matrices

We describe a novel technique for computing a sparse incomplete factorization of a general symmetric positive de nite matrix A. The factorization is not based on the Cholesky algorithm (or Gaussian elimination), but on A-orthogonalization. Thus, the incomplete factorization always exists and can be computed without any diagonal modi cation. When used in conjunction with the conjugate gradient algorithm, the new preconditioner results in a reliable solver for highly ill-conditioned linear systems. Comparisons with other incomplete factorization techniques using challenging linear systems from structural analysis and solid mechanics problems are presented. Copyright ? 2003 John Wiley & Sons, Ltd.