A distributed memory parallel Gauss–Seidel algorithm for linear algebraic systems

Abstract

A distributed memory parallel Gauss–Seidel algorithm for linear algebraic systems is presented, in which a parameter is introduced to adapt the algorithm to different distributed memory parallel architectures. In this algorithm, the coefficient matrix and the right-hand side of the linear algebraic system are first divided into row-blocks in the natural rowwise-order according to the performance of the parallel architecture in use. And then these row-blocks are distributed among local memories of all processors through torus-wrap mapping techniques. The solution iteration vector is cyclically conveyed among processors at each iteration so as to decrease the communication. The algorithm is a true Gauss–Seidel algorithm which maintains the convergence rate of the serial Gauss–Seidel algorithm and allows existing sequential codes to run in a parallel environment with a little investment in recoding. Numerical results are also given which show that the algorithm is of relatively high efficiency.