Parallelizing Strassenʹs method for matrix multiplication on distributed-memory MIMD architectures

We present a parallel method for matrix multiplication on distributed-memory MIMD architectures based on Strassenʹs method. Our timing tests, performed on a 56-node Intel Paragon, demonstrate the realization of the potential of the Strassenʹs method with a complexity of 4.7 M2.807 at the system level rather than the node level at which several earlier works have been focused. The parallel efficiency is nearly perfect when the processor number is the power of 7. The parallelized Strassenʹs method seems always faster than the traditional matrix multiplication methods whose complexity is 2M3 coupled with the BMR method and the Ring method at the system level. The speed gain depends on matrix order M: 20% for M ≈ 1000 and more than 100% for M ≈ 5000.