随机矩阵特征值新盖尔型包含集  

A New Gersgorin-type Eigenvalue Localization Set for Stochastic Matrices

作　　者：朱艳 周宝星 李耀堂[2] ZHU Yan;ZHOU Bao-xing;LI Yao-tang(School of Mathematics,Kunming University,Kunming 650214;School of Mathematics and Statistics,Yunnan University,Kunming 650091)

机构地区：[1]昆明学院数学学院,昆明650214 [2]云南大学数学与统计学院,昆明650091

出　　处：《工程数学学报》2020年第6期771-780,共10页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11861077);the Foundation of Edcucation Commission of Yunnan Province(2011Y011);the Natural Science Foundation of Yunnan Provincial Department of Science and Technology(2019FH001-078);the Research Fund of Kunming University(YJL20019).

摘　　要：随机矩阵及其特征值问题具有广泛的应用背景,计算机辅助几何设计、数理经济学和马尔科夫链等领域都与其有着密切的联系.对随机矩阵特征值问题的研究主要集中在两个方面:在复平面上给出包含随机矩阵所有非1特征值的区域;给出随机矩阵特征值1和非1特征值之间距离的近似值估计.本文对这两方面问题进行了研究,获得了如下结果:通过选择新的参数,获得随机矩阵非1特征值新盖尔型包含区域,改进了近期一些相关成果.并由此得到估计正随机矩阵特征值1与非1特征值距离的新上界算法.最后,数值例子表明算法的优越性.Stochastic matrix and its eigenvalue localization play key roles in many application fields such as computer aided geometric design,mathematical economics and Markov chain.Stochastic matrix eigenvalue problem contains mainly two aspects:providing a region which contains all eigenvalues different from 1 for stochastic matrices in the complex plane;estimating approximately the gap between the dominant eigenvalue 1 and the cluster of all other eigenvalues.In this paper,we localize and estimate the eigenvalues different from 1 of stochastic matrices and obtain the following results:first,we obtain a new and simple region which includes all eigenvalues of a stochastic matrix different from 1 by refining the Ger sgorin circle.Furthermore,an algorithm is proposed to estimate an upper bound for the spectral gap of the subdominant eigenvalue of a positive stochastic matrix.Numerical examples illustrate that the proposed results are effective.

关 键 词：随机矩阵 特征值 非负矩阵 盖尔圆盘 

分 类 号：O151.21[理学—数学]