Performance of a QR algorithm implementation on a multicluster of transputers

Abstract

Some results of an implementation of the QR factorization by Householder reflectors, on a multicluster transputer system with distributed memory are presented, that show how important is the communication time between processor in the performance of the algorithm. The QR factorization was chosen as test method because it is required for many real life applications, for instance in least squares problems. We use a version of Householder transformation that is the basis for numerically stable QR factorization. The machine used was the MultiCluster 2 model of Parsytec which is distributed memory system with 16 Inmos T800 processors. The Helios operating system was chosen because it provides transparency in CPU management. However it limits the sets of connecting topologies to be used. The results are presented in terms of speedup and efficiency, showing the importance of the communication time on the total elapsed time.