Chapter 14 - Adaptive sparse matrix representation for efficient matrix-vector multiplication

Abstract

Sparse matrix-vector multiplication (SpMV) is a fundamental computational kernel used in scientific and engineering applications. The nonzero elements of sparse matrices are represented in different formats, and a single sparse matrix representation is not suitable for all sparse matrices with different sparsity patterns. Extensive studies have been done on improving the performance of sparse matrices processing on different platforms. Graphics processing units (GPUs) are very well suited for dense matrix computations, but most of the existing works on SpMV consider CPUs. In this chapter, we introduce an adaptive GPU-based SpMV scheme that chooses the best representation for the given input matrix based on the configuration and characteristics of GPUs. Our experimental results demonstrate the adaptability of our runtime adaptive scheme on different applications by selecting an appropriate representation for any given input sparse matrix. Compared with the state-of-the-art sparse library and the latest GPU SpMV method, our adaptive scheme improves the performance of sparse matrix multiplications by 2.1× for single-precision and 1.6× for double-precision formats, on average.