SPARSE LINEAR SYSTEMS OF EQUATIONS IN A VECTOR PROCESSING ENVIRONMENT

THIS PROJECT IS TO BUILD A VECTOR PROCESSING VERSION OF PCGPAK, THE PRECONDITIONED CONJUGATE GRADIENT PACKAGE OF SUBROUTINES FOR ITERATIVE SOLUTION OF LARGE, SPARSE, NONSYMMETRIC SYSTEMS OF LINEAR EQUATIONS. THE PCGPAK IS CURRENTLY BEING MARKETED AND IS THE RESULT OF INTERNAL DEVELOPMENT WORK IMPLEMENTING TECHNIQUES FOR ITERATIVE SOLUTION OF SPARSE SYSTEMS DEVELOPED BY RESEARCHERS IN ACADEMIA. PCGPAK REPRESENTS A STATE-OF- THE-ART SOFTWARE TOOL FOR SEQUENTIAL PROCESSING ARCHITEC- TURES, AND ITS MODIFICATION FOR VECTOR PROCESSING EN VIRONMENTS SUCH AS THE CRAY-1 AND CDC CYBER 205 WOULD REPRESENT A MAJOR ADVANCE IN THE SOPHISTICATION AND EFFICIENCY OF SOLUTION TECHNIQUES AVAILABLE ON SUPERCOMPUTERS. THE OBJECTIVE OF THIS RESEARCH WILL BE TO PORT THE CURRENT FORTRAN 77 VERSION OF PCGPAK TO TWO VECTOR PROCESSING SUPERCOMPUTERS: THE CRAY-1 AND THE CYBER 205. THE PERFORMANCE OF THE PRECONDITIONED ITERATIVE ALGORITHMS IN THE VECTOR PROCESSING ENVIRONMENT WILL THEN BE EVALUATED, AND THE MODIFICATION PROCESS OF THOSE ALGORITHMS FOR OPTIMAL PERFORMANCE IN THESE MULTIPROCESSOR ENVIRONMENTS WILL BE BEGUN. THE NEXT STEP WILL BE TO INSTALL PCGPAK ON A VECTOR MULTIPORCESSOR COMPUTER, THE CRAY X/MP, AND BEGIN THE ANALYSIS OF ITS PERFORMANCE IN THE DISTINCTIVE PROCESSING ENVIRONMENT. THIS INSTALLATION WILL REQUIRE SIGNIFICANT HAND-TAILORING OF THE FORTAN CODE TO EXPLICITY SCHEDULE THE PARALLEL EXECUTION OF CODE SEGMENTS. AGAIN, THE PERFORMANCE OF THIS MODIFIED PCGPAK ON A SERIES OF STANDARD PROBLEMS WILL BE PROFILED AND ANALYZED, AND THE PROCESS OF OPTIMIZATION OF THE SERIAL ALGORITHMS FOR THIS ENVIRONMENT WILL BE BEGUN.