Cache friendly sparse matrix-vector multiplication

Abstract

Sparse matrix-vector multiplication or SpMxV is an important kernel in scientific computing. For example, in the conjugate gradient method, where SpMxV is the main computational step. Though the total number of arithmetic operations in SpMxV is fixed, reducing the probability of cache misses per operation is still a challenging area of research. In this work, we present a new column ordering algorithm for sparse matrices. We analyze the cache complexity of SpMxV when A is ordered by our technique. The numerical experiments, with very large test matrices, clearly demonstrate the performance gains rendered by our proposed technique.