Fast Matrix Multiplication Algorithms on Mimd Architectures

Sequential fast matrix multiplication algorithms of Strassen and Winograd are studied; the complexity bound given by Strassen is improved. These algorithms are parallelized on MIMD distributed memory architectures of ring and torus topologies; a generalization to a hyper-torus is also given. Complexity and efficiency are analyzed and good asymptotic behaviour is proved. These new parallel algorithms are compared with standard algorithms on a 128-processor parallel computer; experiments confirm the theoretical results.