Efficient ICCG on a Shared Memory Multiprocessor

In this paper we discuss different approaches for exploiting parallelism in the ICCG method for solving large sparse symmetric positive ,lefinite systems of equations on a shared memory parallel computer. Techniques for efficiently solving triangular systems and computing sparse matrix-vector prodm:ts are explored. Three methods for scheduling the tasks in solving triangular systems are implemented on the Sequent Balance 21000. Sample problems that are row resentative of a large class of problems solved using iterat ive met hods are used. We show that a static analysis to determine data depen,t_mces in the triangular. solve can greatly improve its parallel efficiency. We also show that ignoring symmetry and storing the whole matrix can reduce solution time substantially. "submitted to: International Journal of High Speed Computing. tPh.D. Student at Rensselaer Polytechnic Institute, Troy, NY 12180 and Visiting Research Associate at Research Institute for Advanced Computer Science, NASA Ames Research Center. Moffett Field, CA 940:35. iResearch Institute for Advanced Computer Science, NASA Ames Research (?enter. Moffett Field. CA 94035. °Work reported herein was supported by Cooperative Agreement .N'('C'2-187 between the National .\eronantics and Space Administration (NASA) and the Universities Space Research Association {USRA)..