Factored approximate inverse preconditioners
with dynamic sparsity patterns

Eun-Joo Lee, and Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA

Abstract

We propose two sparsity pattern selection algorithms for factored approximate inverse preconditioners on solving general sparse matrices.

The sparsity pattern is adaptively updated in the construction phase by using combined information of the inverse and original triangular factors of the original matrix.

In order to determine the sparsity pattern, our first algorithm uses the norm of the inverse factors multiplied by the largest absolute value of the original factors, and the second employs the norm of the inverse factors divided by the norm of the original factors.

Experimental results show that these algorithms improve the accuracy and robustness of the preconditioners on solving general sparse matrices.

Key words: Sparse matrix, preconditioning, sparse approximate inverse.

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

Download the PDF file eunjoo-lee4.pdf.

Technical Report 488-07, Department of Computer Science, University of Kentucky, Lexington, KY, 2007.

The research work of Jun Zhang was supported in part by the U.S. National Science Foundation under grant CCF-0527967, in part by the National Institutes of Health under grant 1R01HL086644-01, in part by the Kentucky Science and Engineering Foundation under grant KSEF-148-502-06-186, and in part by the Alzheimer's Association under Grant NIGR-06-25460.