【摘要】 目前关于非负矩阵Perron根即最大特征值的估计和计算已提出了很多方法,利用对角相似变换,给出了一个求非负矩阵Perron根的迭代算法,可以根据精度的要求迭代足够多次得到所需要的近似值,并从理论上证明了它的收敛性,同时给出一种改进的方法,使得在相同的精度下尽可能的减少迭代次数,最后,用数值实例验证。更多还原

【Abstract】 At present,estimation and calculation for Perron root of nonnegative matrices have put forward many methods.This paper gives an iterative algorithm which uses diagonal similarity transformation for Perron root of nonnegative matrices.The algorithm can be achieved through repeated iterative to obtain the needed accuracy.And in theory we prove its convergence.At the same time,this paper gives an improved method which achieves the same accuracy as much as possible to reduce the number of iterations.At last,numerical examples are used to verify this result.更多还原