The Relationship Between the Features of Sparse Matrix and the Matrix Solving Status

Dianwei Han, and Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA
and
Shuting Xu
Department of Computer Information Systems
Virginia State University
Petersburg, VA 23806, USA

Abstract

Solving very large sparse linear systems are often encountered in many scientific and engineering applications. Generally there are two classes of methods available to solve the sparse linear systems. The first class is the direct solution methods, represented by the Gauss elimination method. The second class is the iterative solution methods, of which the preconditioned Krylov subspace methods are considered to be the most effective ones currently available in this field. The sparsity structure and the numerical value distribution which are considered as features of the sparse matrices may have important effect on the iterative solution of linear systems. We first extract the matrix features, and then preconditioned iterative methods are used to the linear system. Our experiments show that a few features that may affect, positively or negatively, the solving status of a sparse matrix with the level-based preconditioners.


Key words: linear systems, iterative methods

Mathematics Subject Classification:


Download the PDF file dianweihan3.pdf.
Technical Report CMIDA-HiPSCCS 001-08, Department of Computer Science, University of Kentucky, Lexington, KY, 2008.

This research was supported in part by the Kentucky Science and Engineering Foundation under the grant KSEF-148-502-05-132.