Abstract
As one of the most essential and important operations in linear algebra, the performance prediction of sparse matrix-vector multiplication (SpMV) on GPUs has got more and more attention in recent years. In 2012, Guo and Wang put forward a new idea to predict the performance of SpMV on GPUs. However, they didn’t consider the matrix structure completely, so the execution time predicted by their model tends to be inaccurate for general sparse matrix. To address this problem, we proposed two new similar models, which take into account the structure of the matrices and make the performance prediction model more accurate. In addition, we predict the execution time of SpMV for CSR-V, CSR-S, ELL and JAD sparse matrix storage formats by the new models on the CUDA platform. Our experimental results show that the accuracy of prediction by our models is 1.69 times better than Guo and Wang’s model on average for most general matrices.
Highlights
Sparse matrix-vector multiplication (SpMV) is an essential operation in solving linear systems and eigenvalue problems
We proposed two new similar models, which take into account the structure of the matrices and make the performance prediction model more accurate
The fraction of the execution time of sparse matrix-vector multiplication (SpMV) may be more than 80% in the total time, so the study of its performance has attracted a lot of attention
Summary
Sparse matrix-vector multiplication (SpMV) is an essential operation in solving linear systems and eigenvalue problems. For irregular matrices, BiELL and BiJAD format can get greater load balance and higher performance by adjusting the elements storage location of matrix and make the zero-padding less They realized CG and GMRES method with BiELL and BiJAD format on GPU [7]. Some benchmark matrices will be generated according to a GPU’s architecture features and four different sparse matrix storage formats, SpMV with these benchmark matrices are implemented on the GPU to obtain the execution times. We will establish two parametric models according to the results of the benchmark matrices and predict the execution time of the SpMV kernels with a given target matrix on the GPU by our models in second phase.
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