發(fā)布時間：2018-10-12 09:15

【摘要】：非負(fù)矩陣?yán)碚撟鳛橐环N基本工具被廣泛應(yīng)用于數(shù)值分析、圖論、計(jì)算機(jī)科學(xué)、管理科學(xué)等領(lǐng)域中.有關(guān)非負(fù)不可約矩陣的譜半徑估計(jì)是該理論的核心問題之一不可約非負(fù)矩陣特征值的算法主要有對角變換法、Perron補(bǔ)集方法、迭代方法等.如果上下界能表示為矩陣元素的易于計(jì)算的函數(shù),那么這種估計(jì)的實(shí)用價值就更高.本文利用Collatz-Wielandt函數(shù)及其推廣,通過研究得到非負(fù)不可約矩陣譜半徑的一個新估計(jì)式：對n(n≥2)階非負(fù)不可約矩陣及任意正整數(shù)κ,記有ρ(A)的估計(jì)式為：進(jìn)一步通過極限研究得出了非負(fù)不可約矩陣譜半徑估計(jì)的一種極限形式：上面的兩個結(jié)論都給出了證明,在計(jì)算上可得到ρ(A)比已有的估計(jì)式有更高精確度的估計(jì)范圍,并用數(shù)值算例驗(yàn)證了這一結(jié)論,特別是ρ(A)的極限式子在理論上會有一定的研究價值.
[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，

本文編號：2265578