Parallel Multiplication of a Vector by a Kronecker Product of Matrices (Part II)

The paper provides a generalization of our previous algorithm for the parallel multiplication of a vector by a Kronecker product of matrices. For any p, a factor of the problem size, our algorithm runs on p processors with a minimum number of communication steps and memory space. Specifically, on p processors with global communication, we show that the multiplication requires at least Θ(log(p)) communication steps, assuming that there is no computation redundancy. This complexity is revised according to the underlying topology, and some performance results on the CRAY T3E are given. keywords Kronecker product, scheduling, communication, complexity. AMS subject classifications. 15A15, 15A09, 15A23