An improvement of SAINV and RIF preconditionings of CG method by double dropping strategy

Preconditioning based on incomplete factorization of the matrix A is among the best known and most popular methods for solving a linear system of equations with symmetric positive definite coefficient matrix. However, the existence of an incomplete factorization is a delicate issue which must be overcame if one has a desire to design reliable preconditioning. Stabilized AINV (approximate in-verse) and RIF (robust incomplete factorization) preconditionings with single dropping have been proposed. Dropping procedure is a key to improvement of efficiency of computation. In this paper, new dropping strategy for improvement of both SAINV and RIF preconditionings are proposed. Moreover comparisons with other incomplete factorization and original SAINV and RIF preconditionings using challenging linear systems from realistic structural analysis are presented. We discuss double dropping strategy in the context of computation time of CG method with preconditioning for successful convergence and memory requirement for factorization.