A row based parallel Gaussian elimination algorithm for the connection machine CM-2

Abstract

This paper presents an algorithm for the Gaussian elimination problem that reduces the length of the critical path compared to the algorithm of Lord et al. This is done by redefining the notion of a task. For all practical purposes, the issues of communication overhead and pivoting cannot be overlooked. We consider these issues for the new algorithm as well. Timing results of this algorithm as executed on the CM-2 model of the Connection Machine are presented. Another contribution of this paper is the use of logical pivoting for stable computation of the Gaussian elimination algorithm. Pivoting is essential is producing stable results. When pivoting occurs, an interchange of two rows is required. A physical interchange of the values can be avoided by providing a permutation vector in a globally accessible location. We show experimental results that substantiate the use of logical pivoting.