Parallel Matrix Multiplication and LU Factorization on Ethernet-Based Clusters

Abstract

This work presents a simple but effective approach for two representative linear algebra operations to be solved in parallel on Ethernet-based clusters: matrix multiplication and LU matrix factorization. The main objectives of this approach are: simplicity and performance optimization. The approach is completed at a lower level by including a broadcast routine based directly on top of UDP to take advantage of the Ethernet physical broadcast facility. The performance of the proposed algorithms implemented on Ethernet-based clusters is compared with the performance obtained with the ScaLAPACK library, which is taken as having highly optimized algorithms for distributed memory parallel computers in general and clusters in particular.