Vol. 54 No. 03 (2005): Volume 54 Number 03, June 2005

Incomplete inverse preconditioners

Department, of Electrical and Computer Engineering, Univercity of Wisconsin, 53706 Madison, USA
Hasan DAĞ
Istanbul Technical University, Faculty of Electrical-Electronics Engineering, Istanbul, Turkey

Published 2005-02-01


  • sparse iterative solvers

How to Cite

ALVARADO, Fernando, and Hasan DAĞ. 2005. “Incomplete Inverse Preconditioners”. ITU ARI Bulletin of Istanbul Technical University 54 (03):48-64. https://ari.itu.edu.tr/index.php/ituari/article/view/63.


Incomplete LU factorization is a valuable preconditioning approach for sparse iterative solvers. An "ideal" but inffcient preconditioner for the iterative solution of Ax = b is A−1itself. This paper describes a preconditioner based on sparse approximations to partitioned representations of A−1, in addition to the results of implementation of the proposed method in a shared memory parallel environment. The partitioned inverses are normally somewhat sparse. Their sparsity can be enhanced with suitable ordering and partitioning algorithms. Sparse approximations to these partitioned inverse representations can be obtained either by discarding selected nonzero entries of these inverses or by precluding the creation of some inversion fills. Experimental results indicate that the use of these partitioned incomplete inverses as preconditioners results in excellent highly parallel preconditioners.