Design and Implementation of a Parallel Algorithm for Solving a Special Linear System using MPI and SHMEM

Abstract

Cholesky factorization is one of the numerically stable methods for the solution of the special linear system of equations, where the system is Symmetric Positive Definite. Tremendous work has been carried out for the parallel implementation of this system on parallel machines and available as a matrix algebra routines. The alternative approach for solution of this system was proposed by Delosme & Ipsen, which avoids sequential forward elimination and back substitution of Cholesky method by a parallel step. In order to implement this algorithm on parallel machines, we require to handle the procedures involved in a slightly different way. These implementation issues are discussed in this paper, in detail. The actual timings for different communication schemes, on different sets of data values and varying number of processors, are tested and reported. In this work we have redesigned and implemented the algorithm using different communication possibilities namely Message Passing Interface (MPI) and Shared Memory routines (SHMEM) and compared the results. To the best of our knowledge, this is the first effort to implement this algorithm using these communication routines. © 2002 Taylor & Francis Group, LLC.