基于CUDA实现MRRR算法并行

Parallel Realization of the MRRR Algorithm Based on CUDA

MRRR(Multiple Relatively Robust Representations)算法是求解对称三对角矩阵本征值问题高效、精确的算法之一。在分析MRRR算法及CUDA(Compute Unified Device Architecture)并行体系结构的基础上,针对算法的可并行性,采用单指令多线程并行方式实现了基于CUDA的MRRR算法并行,并从存储结构方面优化算法。实验结果显示,与LAPACK库中串行MRRR实现相比,并行方法在保证精度的基础上获得了20倍的加速比,进而从计算精度和计算时间上说明MRRR算法适合在GPU上并行。

The algorithm of multiple relatively robust representations（MRRR） is one of the fastest and most accurate algorithms. After analyzing the MRRR algorithm and CUDA parallel architecture, parallel MRRR algorithm based on CUDA was given, and explored the optimization in memory structure. Compared with LAPACK＇s MRRR implementation this parallel method provides 20-fold speedups. This result demonstrates the algorithm can be mapped efficiently onto GPU.