A parallel elimination algorithm for the solution of dense linear systems

Abstract

For the solution of an N × N linear system Ax = d, based on the folding method of Evans and Hatzopoulos [4] and by partitioning the system into r 2 blocks each of size n × n (N = r n), in [3] we had described a parallel elimination method suitable for an r-processor machine. The serial arithmetical operations count for this algorithm is 0(1/3(3 − l/r)N 3) thereby the algorithm could perform with efficiency E r = 2/(3 − 1/r); note that 2/3 ≤ Er ≤ 4/5. In the present paper we consider an alternative elimination procedure together with the method of partitioning to obtain a parallel algorithm for the solution of dense linear systems. The serial arithmetical operations count for the present algorithm is 0(2/3N 3), which is of the same order as that for the standard Gaussian elimination method; thus the present algorithm could perform with efficiency close to 1 on a multiprocessor machine.