Ordering Methods for Sparse Matrices.

Abstract

Abstract : The solution of systems of large sparse linear equations is a fundamental computational step in the numerical solution of many scientific and engineering problems. These problems arise in such diverse areas as electromagnetic pulse (EMP) analysis, structural analysis, linear programming, network analysis, chemical process design, optimization, steady state analysis, and policy planning. When direct solution methods are used to solve these equations one of the major difficulties is choosing a reordering of the rows and columns. Because sparse matrix research has grown independently out of many disciplines, there are many heuristic methods (band, profile, Markowitz, tearing, P(4), and variations) presently used to accomplish this reordering. The challenge in building standard software is to determine if one heuristic works must be available in a general purpose code. If several heuristics are needed, matrix classes must be identified as a basis for matching a given matrix with the proper ordering method. In either case it must also be determined how much performance will improve for particular problem classes if specialized sparse matrix code rather than general purpose code is used. This research project is concerned with answering these questions. This report describes the current status of the project.