求对称方阵特征值的一种快速并行算法

Quick Algorithm of Sloving Eigenvalue of Symmetric Matrix

该文针对经典雅可比算法求对称矩阵特征值不但要选主元素,而且还要同时进行行、列旋转变换、数据相关关系复杂、额外计算开销大、不易并行的缺点,提出了一种基于矩阵单侧旋转的算法并对此算法进行分析。最后通过该算法在PC机和分布式存储的大规模并行处理机曙光1000上的实验数据对比验证了该算法的性能较雅可比算法优越。

The process of computing the eigenvalue of symmetric matrix using Jacobi algorithm exists not only the overhead of choosing the pivot,but also the double rotation transformations on row and column ,which makes the data dependencies very complex and unsuitable for parallel computing.This paper gives a method by using the one -side rotation to compute the eigenvalue of the symmetric matrix.By comparing the new method with Jacobi algorithm on both personal computer and MPP Dawn-1000,it is proved that the method is much superior.