非负矩阵谱半径的一个新界值估计

Estimation of new bounds on the spectral radius of nonnegative matrix

对非负矩阵谱半径的界值给出了一个新的估计,把非负矩阵谱半径的上下界表示成矩阵元素的一个易于计算的函数,证明了由该函数表示的谱半径的上下界可以通过递推计算的方法无限地逼近谱半径.最后,通过实例与以往的结论作比较,验证了该界值估计的有效性.

In this paper, a new method of estimating is given for the upper and lower bounds on the spectral radius of a nonnegative matrix, which is expressed as an easily calculated function in element of matrix. It was proved that the upper and lower bounds of the spectral radius expressed by the function can approximate the spectral radius infinitely through recurrence calculation. Compared with the related results, it was tested the service quality of the estimation.