A Comparative Study on Dynamic and Static Sparsity
Patterns in Parallel Sparse Approximate Inverse Preconditioning

Kai Wang, Sangbae Kim, and Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA


Sparse approximate inverse (SAI) techniques have recently emerged as a new class of parallel preconditioning techniques for solving large sparse linear systems on high performance computers. The choice of the sparsity pattern of the SAI matrix is probably the most important step in constructing an SAI preconditioner. Both dynamic and static sparsity pattern selection approaches have been proposed by researchers. Through a few numerical experiments, we conduct a comparable study on the properties and performance of the SAI preconditioners using the different sparsity patterns for solving some sparse linear systems.

Key words: parse matrices, parallel preconditioning, sparse approximate inverse, dynamic and static sparsity pattern.

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

Download the compressed postscript file saicomp.ps.gz, or the PDF file saicomp.pdf.gz.
This paper has been published in Journal of Mathematical Modeling and Algorithms, Vol. 2, No. 2, pp. 203--215, 2003.

Technical Report 361-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002.

This research work supported in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, CCR-0092532, and ACI-0202934, in part by the U.S. Department of Energy Office of Sceince under grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology, and in part by the University of Kentucky Research Committee.