We develop new concepts and parallel algorithms of multistep successive preconditioning strategies to enhance efficiency and robustness of standard sparse approximate inverse preconditioning techniques. The key idea is to compute a series of simple sparse matrices to approximate the inverse of the original matrix. Studies are conducted to show the advantages of such an approach in terms of both improving preconditioning accuracy and reducing computational cost. Numerical experiments using one prototype implementation to solve a few general sparse matrices on a distributed memory parallel computer are reported.

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

Previously published as Technical Report 331-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002. Download the compressed postscript file multisail.ps.gz, or the PDF file multisail.pdf.

This research was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, and CCR-0092532, in part by the Japanese Research Organization for Information Science & Technology, and in part by the University of Kentucky Research Committee.