Sparse Matrix Formats Evaluation and Optimization on a GPU

The data parallel programming model comes back with massive multicore architectures. The GPU is one of these and offers important possibilities to accelerate linear algebra. However, the irregular structure of sparse matrix operations generates problems with this programming model to obtain efficient performance. This depends on the used format to store values and the matrix structure. The sparse matrix-vector product (SpMV) is one of the most used kernel in scientific computing and is the main performance source of iterative methods. We propose an evaluation and optimization of several sparse formats for the SpMV kernel which have succeeded at the time of data parallel computer. This study is realized by analyzing the performances following the distribution of the non zeros values in the matrix to determine the best and the worst reachable value. The results show that all sparse formats converge to the same efficiency and perform poorly with a strong distribution of elements.