非负不可约矩阵谱半径的估计

Estimation of spectral radius of nonnegative irreducible matrices

为给出非负不可约矩阵的谱半径上、下界的新估计,首先构造一个新的矩阵形式及两个收敛的序列,之后利用矩阵特征值和特征向量的关系,进一步给出非负不可约矩阵谱半径的易于计算的上、下界.最后通过数值实例验证了所得结论的有效性.

In order to give a new estimate of the upper and lower bounds of spectral radius for nonnegative irreducible matrices,a new matrix form and two convergent sequences firstly are constructed.Secondly,the upper and lower bounds of the spectral radius of nonnegative irreducible matrices are given by use of the relationship between eigenvalues and eigenvectors,which are easy be calculated.Finally,some numerical examples are used to verify the validity of the conclusions.