不可约非负矩阵的最大特征值估计

Estimation for the Maximal Eigenvalue of Irreducible Nonnegative Matrix

利用不可约非负矩阵和Collatz—Wielandt函数的性质,给出了非负不可约矩阵最大特征值的一些界。比较这些界的大小,利用极限的思想得到了求非负不可约矩阵最大特征值的方法。利用这种方法可以去估计非负不可约矩阵最大特征值的大小,并通过计算和比较,验证了这种估计方法是可行的。

In the paper, based on the property of irreducible nonnegative matrix and CollatzWielandt function, we derive some bounds for the maximal eigenvalue of irreducible nonnegative matrix. The method of seeking for the maximal eigenvalue of irreducible nonnegative matrix is given by the size of these bounds and the idea of limit. We can use this method to estimate the maximal eigenvalue of irreducible nonnegative matrix. It is proved that this estimation is feasible by calculating and comparing.