Information theoretic approach to the Perron root of nonnegative irreducible matrices
Information theoretic approach to the Perron root of nonnegative irreducible matrices
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非负不可约矩阵 Perron 根的信息论方法
DOI：
10.1109/itw.2004.1405310
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
H. Boche
中科院分区：
文献类型：
--
作者：
S. Stańczak;H. Boche
本文利用Kullback-Leibler距离（推广到正离散测度）刻画了非负不可约矩阵的Perron根.根据Perron-Frobenius理论，任何非负不可约矩阵的Perron根等于其谱半径。因此，本文建立了信息论和线性代数的两个基本概念之间的联系。此外，这些结果被证明有有趣的应用，在无线通信网络中的经典功率控制问题。最后，我们证明了新的鞍点特征的Perron根，并提出可能的扩展结果更一般的功能。
This paper characterizes the Perron root of nonnegative irreducible matrices in terms of the Kullback Leibler distance (generalized to positive discrete measures). By Perron-Frobenius theory, the Perron root of any nonnegative irreducible matrix is equal to its spectral radius. Thus, the paper establishes a connection between two fundamental concepts of information theory and linear algebra. Moreover, these results are shown to have interesting applications to the classical power control problem in wireless communications networks. Finally, we prove new saddle point characterizations of the Perron root and present possible extensions of the results to more general functions.