Tuning matrix-vector multiplication on GPU

A matrix times vector multiplication (matvec) is a cornerstone operation in iterative methods of solving large sparse systems of equations such as the conjugate gradients method (cg), the minimal residual method (minres), the generalized residual method (gmres) and exerts an influence on overall performance of those methods. An implementation of matvec is particularly demanding when one executes computations on a GPU (Graphics Processing Unit), because using this device one has to comply with certain programming rules in order to take advantage of parallel computing. In this paper, it will be shown how to modify the sparse matrix-vector multiplication based on CRS (Compressed Row Storage) to achieve about 3-5 times better performance on - a low cost - GPU (GeForce GTX 285, 1.48 GHz) than on a CPU (Intel Core i7, 2.67 GHz).