A parallel software package for solving linear systems

Abstract

A problem arising in scientific computation is the solution of Ax=b, where A is a large, sparse matrix. One of the most robust algorithms for solving the above equation is the conjugate gradient method, especially when combined with a preconditioner. The authors discuss a new software package, MP-PCGPAK2, that implements a parallel version of the conjugate gradient method for MIMD (multiple-instruction multiple-data), message passing architectures. The parallel implementation is quite general and can be applied to algorithms for nonsymmetric or indefinite systems such as GMRES, Bi-CGSTAB, and QMR. The authors present results on a 1024 processor nCUBE 2, and a 128 processor iPSC/860, for positive definite, symmetric systems ranging from one million to over 11 million variables.<>