Polynomial preconditioners based on factorized sparse approximate inverses

摘要

Let Ax=b be a linear system where A is a symmetric positive definite matrix. An additive polynomial preconditioner for the Conjugate Gradient method based on multisplittings is proposed. The multisplittings are obtained by computing some factorized sparse approximate inverses of the coefficient matrix. Namely, splittings of the form A=(Z̄Z̄T)−1−N,Z̄Z̄T≈A−1 induced by the AINV and FSAI factorized approximate inverse preconditioners applied to diagonal blocks of A are used. The applicability of this preconditioner is studied. Moreover, the results of the numerical experiments obtained on a Cray T3E for a representative set of matrices are presented. Specifically, structural analysis and transport/diffusion problems are considered. The effect of the Reverse Cuthill–McKee (RCM) and Multiple Minimum Degree (MMD) orderings is evaluated.