A PROPOSAL FOR BUILDING A SOFTWARE PACKAGE FOR SOLVING LARGE, SPARSE LINEAR SYSTEMS OF EQUATIONS IN A VECTOR PROCESSING ENVIRONMENT

OUR OUTLINED PLANS TO BUILD A VECTOR PROCESSING VERSION OF PCGPAKTM, THE PRECONDITIONED CONJUGATE GRADIENT PACKAGE OF SUBROUTINES FOR INTERATIVE SOLUTION OF LARGE, SPARSE, NONSYMMETRIC SYSTEMS OF LINEAR EQUATIONS. PCGPAK, WHICH IS CURRENTLY BEING MARKETED BY SCIENTIFIC COMPUTING ASSOCIATES, REPRESENTS A STATE-OF-THE-ART SOFTWARE TOOL FOR SEQUENTIAL PROCESSING ARCHITECTURES, AND ITS MODIFICATION FOR VECTOR PROCESSING ENVIRONMENTS WOULD REPRESENT A MAJOR ADVANCE IN THE SOPHISTICATION AND EFFICIENCY OF SOLUTION TECHNIQUES AVAILABLE ON SUPERCOMPUTERS. THE OBJECTIVE FOR PHASE I WILL BE TO PORT THE CURRENT FORTRAN77 VERSION OF PCGPAK TO A COMMERCIALLY-AVAILABLE VECTOR PROCESSING SUPERCOMPUTER, SUCH AS THE FPS X64 SERIES OR THE CRAY X/MP. WILL THEN EVALUATE THE PERFORMANCE OF THE PRECONDITIONED ITERATIVE ALGORITHMS IN THIS VECTOR PROCESSING ENVIRONMENT. A SECOND MAJOR OBJECTIVE OF PHASE I WILL BE TO DETERMINE HOW THESE BENCHMARKS VARY FOR DIFFERENT TYPES OF PROBLEMS. THE REDESIGN AND MODIFICATION OF ALGORITHMS WILL OCCUR DURING PHASE II. DURING THIS PHASE, IMPLEMENTATION OF BETTER LOW LEVEL MATRIX ARITHMETIC ROUTINES, SUCH AS MATRIX-VECTOR AND VECTOR-MATRIX MULTIPLICATIONS, WILL BE IMPLEMENTED, AS WELL AS MORE FUNDAMENTAL REORGANIZATION OF THE DATA STRUCTURE AND ALGORITHMS FOR ITERATIVE SOLUTION.