大规模稀疏矩阵的主特征向量计算优化方法

Optimization of Parallel Principal Eigenvectors Computing for Large-Scale Sparse Matrixes

矩阵主特征向量(principal eigenvectors computing,PEC)的求解是科学与工程计算中的一个重要问题。随着图形处理单元通用计算(general-purpose computing on graphics pro cessing unit,GPGPU)的兴起,利用GPU来优化大规模稀疏矩阵的图形处理单元求解得到了广泛关注。分别从应用特征和GPU体系结构特征两方面分析了PEC运算的性能瓶颈,提出了一种面向GPU的稀疏矩阵存储格式——GPU-ELL和一个针对GPU的线程优化映射策略,并设计了相应的PEC优化执行算法。在ATI HD Radeon5850上的实验结果表明,相对于传统CPU,该方案获得了最多200倍左右的加速,相对于已有GPU上的实现,也获得了2倍的加速。

The principal eigenvectors computing （PEC） is a paramount operation in engineering and scientific computing. Since the general-purpose computing on graphics processing unit （GPGPU） emerges for the outstanding acceleration factors, PEC implementations on graphics processing unit （GPU） have appeared on the scene. This paper analyzes PEC performance bottleneck from the characteristic of application and GPU architecture, and thereforeproposes a new implementation of PEC based on a new matrix storage format, called GPU-ELL, and an optimized thread mapping strategy of GPU. It evaluates the proposed approach over ATI HD Radeon 5850 GPU, and the ex- perimental results show its good performance with average 200 times acceleration of other existing algorithm on CPU, and 2 times of that on GPU.