A Note on the Performance of Sparse Matrix-vector Multiplication with Column Reordering

We revisit ordering techniques as a preprocessing step for improving the performance of sparse matrix-vector multiplication (SpM x V) on modern hierarchical memory computers. In computing SpM x V the main purpose of ordering of columns (or rows) is to improve the performance by enhancing data reuse. We present a new ordering technique based on the binary reflected gray codes and experimentally evaluate and compare it with other column ordering techniques from the literature. The results from numerical experiments with very large test matrices clearly demonstrates the performance gains rendered by our proposed technique.