计算Pascal矩阵谱半径和相应特征向量的一个快速算法

A Fast Algorithm for Computing the Spectral Radius and the Correspondent Eigenvector of the Pascal Matrices

研究Pascal矩阵谱半径及其对应特征向量的数值求解算法问题,利用幂法和Pascal矩阵的性质给出了一个有效的迭代求解算法,该算法每一步迭代只用到浮点数的加法运算。同时数值实验显示,该算法具有较高的精度和较快的收敛速度。

The problem for computing the spectral radius and its correspondent eigenvector has been considered. An efficient fast algorithm has bee presented, by using the power method and the algebraic properties of Pascal matrices. The new algorithm needs only additions without multiplication at each iteration step. The numerical experiments show that the accuracy and the convergent speed of the new algorithm are sound.