非负不可约矩阵谱半径估计的一种极限方法
发布时间：2018-10-12 09:15
【摘要】：非负矩阵理论作为一种基本工具被广泛应用于数值分析、图论、计算机科学、管理科学等领域中.有关非负不可约矩阵的谱半径估计是该理论的核心问题之一不可约非负矩阵特征值的算法主要有对角变换法、Perron补集方法、迭代方法等.如果上下界能表示为矩阵元素的易于计算的函数,那么这种估计的实用价值就更高.本文利用Collatz-Wielandt函数及其推广,通过研究得到非负不可约矩阵谱半径的一个新估计式：对n(n≥2)阶非负不可约矩阵及任意正整数κ,记有ρ(A)的估计式为：进一步通过极限研究得出了非负不可约矩阵谱半径估计的一种极限形式：上面的两个结论都给出了证明,在计算上可得到ρ(A)比已有的估计式有更高精确度的估计范围,并用数值算例验证了这一结论,特别是ρ(A)的极限式子在理论上会有一定的研究价值.
[Abstract]:As a basic tool, non-negative matrix theory is widely used in the fields of numerical analysis, graph theory, computer science, management science and so on. The estimation of spectral radius of nonnegative irreducible matrices is one of the core problems in this theory. The main algorithms for eigenvalues of irreducible nonnegative matrices are diagonal transformation method, Perron complement method, iterative method and so on. If the upper and lower bounds can be expressed as computable functions of matrix elements, the practical value of this estimate is even higher. In this paper, by using Collatz-Wielandt function and its generalization, By studying a new estimate of spectral radius of nonnegative irreducible matrix: n (n 鈮，
本文编号：2265578
[Abstract]:As a basic tool, non-negative matrix theory is widely used in the fields of numerical analysis, graph theory, computer science, management science and so on. The estimation of spectral radius of nonnegative irreducible matrices is one of the core problems in this theory. The main algorithms for eigenvalues of irreducible nonnegative matrices are diagonal transformation method, Perron complement method, iterative method and so on. If the upper and lower bounds can be expressed as computable functions of matrix elements, the practical value of this estimate is even higher. In this paper, by using Collatz-Wielandt function and its generalization, By studying a new estimate of spectral radius of nonnegative irreducible matrix: n (n 鈮，
本文编号：2265578
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