非负矩阵Perron根与主特征向量的粒子迭代算法  

Particle iterative algorithm for non-negative matrix Perron root and principal eigenvector

作　　者：曾莉[1] 肖明[1] ZENG Li;XIAO Ming(School of Computer Science and Technology,Southwest Minzu University,Chengdu 610041,P.R.C.)

机构地区：[1]西南民族大学计算机科学与技术学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2020年第1期71-76,共6页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：西南民族大学中央高校基本科研业务费专项资金项目资助(2014NZYQN33)。

摘　　要：非负矩阵Perron根问题在数值分析、经济学及控制论等多方面有着重要的应用,如何快速求出非负矩阵Perron根与主特征向量,一直是矩阵理论研究的热点.结合矩阵Perron根和主特征向量的特性,给出基于粒子迭代的快速寻优算法,同时给出该方法的收敛性的证明,最后通过数值实验说明了该方法的优越性.Perron root problem of non-negative matrix has important applications in numerical analysis,economics and cybernetics,etc.How to quickly find the values of Perron root of non-negative matrix and corresponding eigenvectors has always been the focus of matrix theory research.Combining the characteristics of Perron root of matrix and principal eigenvector,a fast optimization algorithm based on particle iteration is given.At the same time,the convergence of the method is proved.Finally,the advantages of the method are illustrated by numerical experiments.

关 键 词：非负矩阵 PERRON根 特征向量 粒子群算法 

分 类 号：O24[理学—计算数学]