Rational approximation preconditioners for sparse linear systems.
This paper deals with incomplete LU factorization preconditioners of very ill-conditioned matrices. A class of preconditioning techniques is presented. The idea is exploiting a rational approximation to the inverse of the shifted original matrix and then an incomplete LU factorization of the resulting matrix is computed. The resulting factors are then used to compute a better preconditioner for the original matrix. As a good LU factorization can be obtained without allowing much fill-in, the main motivation for this process is to save memory. A theoretical analysis and numerical experiments are presented to show that the resulting method can succeed in solving rather difficult problems.
scientific article; zbMATH DE number 1993224
scientific article