Approximate Inverse for Indefinite Matrices

Laboratory for High Performance Scientific Computing and Computer Simulation

Department of Computer Science

University of Kentucky

Lexington, KY 40506-0046, USA

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 approximate inverse matrices produced from each phase are then combined to be used as a preconditioner for the original matrix. 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 some indefinite matrices.

**Mathematics Subject Classification**: 65F10, 65F50, 65N55, 65Y05.

Download the PDF file eunjoo-lee3.pdf.

Technical Report 476-07, Department of Computer Science, University of Kentucky, Lexington, KY, 2007.

The authors' research work were supported in part by the U.S. National Science Foundation under grants CCR-0092532 and CCF-0527967, in part by the Kentucky Science and Engineering Foundation under grants KSEF-148-502-05-132 and KSEF-148-502-06-186, and in part by the Alzheimer's Association under a New Investigator Research Grant NIGR-06-25460.