Efficient broadcasts and simple algorithms for parallel linear algebra computing in clusters

This paper presents a natural and efficient implementation for the classical broadcast message passing routine which optimizes performance of Ethernet based clusters. A simple algorithm for parallel matrix multiplication is specifically designed to take advantage of both, parallel computing facilities (CPUs) provided by clusters, and optimized performance of broadcast messages on Ethernet based clusters. Also, this simple parallel algorithm proposed for matrix multiplication takes into account the possibly heterogenous computing hardware and maintains a balanced workload of computers according to their relative computing power. Performance tests are presented on a heterogenous cluster as well as on a homogeneous cluster, where it is compared with the parallel matrix multiplication provided by the ScaLAPACK library. Another simple parallel algorithm is proposed for LU matrix factorization (a general method to solve dense systems of equations) following the same guidelines used for the parallel matrix multiplication algorithm. Some performance tests are presented over a homogenous cluster.