SpMV is an essential kernel existing in many HPC and data center applications. Meanwhile, the emerging many-core hardware provides promising computational power, and is widely used for acceleration. Many methods and formats have been proposed aiming at better performance of SpMV on many-core platforms. However, there is still lack of a comprehensive comparison of SpMV methods to show their performance difference on sparse matrices with various sparse patterns. Moreover, there is still no systematic work to bridge the gap between SpMV performance and sparse pattern.

In this paper, we investigate the performance of 27 SpMV methods with 1500+ sparse matrices on two many-core platforms: Intel Xeon Phi (Knights Landing 7250) and Nvidia GPGPU (Tesla M40). Our work shows that no single SpMV methods is optimal for all sparse patterns, but some methods can achieve approximately the best performance on most sparse matrices. We further select 13 features to describe the sparse pattern and analyze their correlations to the performance of each SpMV method. Our observations should help other researchers and practitioners to better understand the SpMV performance and provide implications to guide the selection of suitable SpMV method.