In this paper, we analyse the Perron vector of an irreducible nonnegative tensor, and present some lower and upper bounds for the ratio of the smallest and largest entries of a Perron vector based on some new techniques, which always improve the existing ones. Applying these new ratio results, we first refine two-sided bounds for the spectral radius of an irreducible nonnegative tensor. In particular, for the matrix case, the new bounds also improve the corresponding ones. Second, we provide a new Ky Fan type theorem, which improves the existing one. Third, we refine the perturbation bound for the spectral radii of nonnegative tensors, from which one may derive a comparison theorem for spectral radii of nonnegative tensors. Numerical examples are given to show the efficiency of the theoretical results.

中文翻译：

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不可约非负张量的Perron向量分析及其应用

在本文中，我们分析了不可约非负张量的Perron向量，并基于一些新技术提出了Perron向量最小和最大项之比的上下限，这些新技术总是会改进现有技术。应用这些新的比率结果，我们首先针对不可约非负张量的谱半径细化了两个边界。特别是对于矩阵情况，新边界也会改善相应边界。其次，我们提供了一个新的Ky Fan型定理，它对现有定理进行了改进。第三，我们细化了非负张量谱半径的摄动界，从中可以得出非负张量谱半径的比较定理。数值算例表明了理论结果的有效性。