Automatic Tuning of Sparse Matrix-Vector Multiplication for CRS Format on GPUs

Performance of sparse matrix-vector multiplication (SpMV) on GPUs is highly dependent on the structure of the sparse matrix used in the computation, the computing environment, and the selection of certain parameters. In this paper, we show that the performance achieved using kernel SpMV on GPUs for the compressed row storage (CRS) format depends greatly on optimal selection of a parameter, and we propose an efficient algorithm for the automatic selection of the optimal parameter. Kernel SpMV for the CRS format using automatic parameter selection achieves up to approximately 26% improvement over NVIDIA's CUSPARSE library. The conjugate gradient method is the most popular iterative method for solving sparse systems of linear equations. Kernel SpMV makes up the bulk of the conjugate gradient method calculations. By optimizing SpMV using our approach, the conjugate gradient method performs up to approximately 10% better than CULA Sparse.