The lower and upper bounds on Perron root of nonnegative irreducible matrices
The lower and upper bounds on Perron root of nonnegative irreducible matrices
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非负不可约矩阵 Perron 根的下界和上限
DOI：
10.1016/j.cam.2007.06.034
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发表时间：
2008
影响因子：
2.4
通讯作者：
Ke Guo
中科院分区：
文献类型：
--
作者：
G. Huang;F. Yin;Ke Guo
设A是一个n×n非负不可约矩阵，A[α]是A基于{1，2，.，n}的非空有序子集α的主子矩阵，用Pt（A/A[α]）定义A[α]的广义Perron补，即，本文给出了A的Perron根的上、下界。由给定参数t0的最大值和[公式：见正文]的行和的最大值导出Perron根的上界，同时由给定参数t0的最小值和[公式：见正文]的行和的最小值表示Perron根的下界.同时也给出了如何在α之后选择参数t以得到ρ（A）的更紧的上下界.数值算例表明，本文方法与文献[L. Z. Lu，M.K. Ng，Perron根的位置，线性代数应用392（2004）103-117。]更有效。
Let A be an n×n nonnegative irreducible matrix, let A[α] be the principal submatrix of A based on the nonempty ordered subset α of {1,2,…,n}, and define the generalized Perron complement of A[α] by Pt(A/A[α]), i.e., This paper gives the upper and lower bounds on the Perron root of A. An upper bound on Perron root is derived from the maximum of the given parameter t0and the maximum of the row sums of [Formula: see text] , synchronously, a lower bound on Perron root is expressed by the minimum of the given parameter t0and the minimum of the row sums of [Formula: see text] . It is also shown how to choose the parameter t after α to get tighter upper and lower bounds of ρ(A). Several numerical examples are presented to show that our method compared with the methods in [L.Z. Lu, M.K. Ng, Locations of Perron roots, Linear Algebra Appl. 392 (2004) 103–117.] is more effective.