Exploiting Data Sparsity in Parallel Matrix Powers Computations

We derive a new parallel communication-avoiding matrix powers algorithm for matrices of the form A = D + USV H , where D is sparse and USV H has low rank and is possibly dense. We demonstrate that, with respect to the cost of computing k sparse matrix-vector multiplications, our algorithm asymptotically reduces the parallel latency by a factor of O(k) for small additional bandwidth and computation costs. Using problems from real-world applications, our performance model predicts up to 13× speedups on petascale machines.