基于CUDA的大型实对称矩阵并行求逆算法

CUDA-based parallel matrix inverse algorithm of large-scale real symmetric matrix

针对大型实对称矩阵数值求逆算法运算量大、计算时间长的问题,分析分块迭代求逆算法的并行性,设计基于CUDA(compute unified device architecture)的并行求逆算法。设计对比分析实验,实验结果表明,该算法能够提高大型实对称矩阵求逆的速度,当矩阵大小为8000×8000时,加速比高达279倍,很好满足了实际工程中对实时性要求高的需求,且计算精度基本保持不变。

Some problems including the huge amount of computations and time-consumption exit in the process of computing the inverse matrix of a large real symmetric matrix using block-based iterative inversion algorithm. To solve these problems, a paral- lel analysis of the iterative inversion algorithm was made, and then it was optimized based on CUDA. The comparison between the sequential algorithm and the parallel one was designed. The experimental result shows that the parallel algorithm is able to improve the speed of the algorithm greatly. When the size of matrix is 8000 × 8000, the speedup is 279 times. Hence this parallel algorithm can meet the high real-time requirement well in actual applications, while maintaining almost the same accuracy.