A two-phase preconditioning strategy of sparse approximate inverse for indefinite matrices

A two-phase preconditioning strategy based on a factored sparse approximate inverse is proposed for solving sparse indefinite matrices. In each phase, the strategy first makes the original matrix diagonally dominant to enhance the stability by a shifting method, and constructs an inverse approximation of the shifted matrix by utilizing a factored sparse approximate inverse preconditioner. The two inverse approximation matrices produced from each phase are then combined to be used as a preconditioner. Experimental results show that the presented strategy improves the accuracy and the stability of the preconditioner on solving indefinite sparse matrices. Furthermore, the strategy ensures that convergence rate of the preconditioned iterations of the two-phase preconditioning strategy is much better than that of the standard sparse approximate inverse ones for solving indefinite matrices.