Parallelization of Padé Approximation of Matrix Exponential with CUDA-Aware MPI

Matrix exponential has many applications in science and engineering, including in the solution of differential equations and transient analysis of continuous-time Markov chains. One of the best methods for computing matrix exponential is via Padé approximation combined with scaling and squaring. In this paper we propose a method for parallelizing this Padé approximation of matrix exponential by performing its computation on a cluster of computers equipped with graphic processing units connected by CUDA-aware message passing interface. The main purpose of this parallelization is to allow for the computation of exponential of large matrices that may no longer fit in memory, while still retaining reasonable speed. Experimental results show that the proposed method can solve large matrices faster with increasing number of computer nodes. However, the results also show that communication time has the most significant effect on the computation time.