Accelerating the general band matrix multiplication using graphics processors

In this paper, we leverage the intrinsic data-parallelism of the band matrix-matrix product to accelerate this operation on Graphics Processing Units (GPUs). In particular, we propose a Level-3 BLAS style algorithm to tackle the band matrix-matrix product and implement two GPU-based versions that off-load the most expensive computations - i.e., general dense matrix-matrix multiplication, triangular matrixmatrix multiplication and matrix addition - to the hardware accelerator. Results collected using GPUs for the two most recent generations of NVIDIA (“Fermi” and “Kepler”) and a complete set of benchmark cases (which differ in the matrix dimensions and bandwidth) show that the GPU-enabled implementations deliver a notable reduction of the execution time.