Scalability of Hybrid Sparse Matrix Dense Vector (SpMV) Multiplication

SpMV, the product of a sparse matrix and a dense vector, is emblematic of a new class of applications that are memory bandwidth and communication, not flop, driven. Sparsity and randomness in such computations play havoc with conventional implementations, especially when strong, instead of weak, scaling is attempted. This paper studies improved hybrid SpMV codes that have better performance, especially for the sparsest of such problems. Issues with both data placement and remote reductions are modeled over a range of matrix characteristics. Those factors that limit strong scalability are quantified.