The Parallel Solution of Triangular Systems of Equations

In this paper, methods are presented for the parallel solution of (n × n) lower triangular linear systems suitable for a p processor MIMD computer system where n/2 < p < (n − 1). The methods are based on the principle of allocating the processors as soon as they become available, thus creating a wavefront through the triangular array. The algorithms are shown to run in time (4n − 3p − 2) for p < 2( n − 1)/3 and in time 2(n − 1) for p ≥ 2(n − 1)/3.