A Parallel Modified Block Lanczos' Algorithm for Distributed Memory Architectures

In this paper we propose a parallel block Lanczos algorithm suitable for MIMD distributed memory message passing architectures. We first consider a direct parallelization of the classic block Lanczos algorithm and we evaluate its performance. Then, after a discussion of these results, we reorganize the block algorithm obtaining a modified version that has a better behaviour with respect to the performance in the considered computing environment. We assume a unidirectional ring as connection topology and a block column wrap-around matrices distribution. We have chosen this approach to improve load-balancing, to eliminate the intersection of messages and to decrease communication. The two parallel block Lanczos algorithms have been tested on a Convex Meta Series, a cluster of HP Series 9000 workstations, running the PVM communication system.