非负矩阵Perron根的一种迭代改进算法  

An iterative improvement algorithm for Perron root of nonnegative matrices

作　　者：曾莉[1] 肖明[1] 

机构地区：[1]西南民族大学计算机科学与技术学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2013年第1期30-33,共4页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：西南民族大学中央高校基本科研业务费专项资金项目资助(12NZYQN21)

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.At present, many methods have been put forward for the estimation and calculation of Perron root of nonnegative matrices. This paper gives an iterative algorithm which uses diagonal similarity transformation for Perron root ofnonnegative matrices. The algorithm can be achieved through repeated iterative to obtain the needed accuracy. And in theory this paper proves its convergence. At the same time, an improved method is given 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.

关 键 词：非负矩阵 PERRON根 迭代 

分 类 号：O151.21[理学—数学]