非负不可约矩阵Perron根的一个下界

A lower bound for Perron root of irreducible nonnegative matrices

根据非负不可约矩阵谱半径(Perron根)的相关性质,得到其Perron根的一个新下界,证明了当矩阵对称时新下界较经典下界更优,数值算例进一步验证了其有效性。

The bound for the Perron root of nonnegative matrices is discussed. A lower bound is obtained for the Perron root of nonnegative matrices. It is proved that the new lower bound is better than the classical lower bound when the matrix is symmetric. Some numerical examples are proposed at last.