非负不可约矩阵Perron根的估计  

Estimations for the Perron Root of Irreducible Nonnegative Matrices

作　　者：廖平[1] 王龙[1] 赵丹[1] 

机构地区：[1]四川职业技术学院应用数学与经济系,四川遂宁629000

出　　处：《数学的实践与认识》2015年第17期292-296,共5页Mathematics in Practice and Theory

基　　金：四川省教育厅自然科学青年基金项目(13ZB0033)

摘　　要：给出了非负不可约矩阵Perron根的一些上下界估计,设A为任意非负不可约矩阵,ρ(A)为其Perron根,则ρ(A)≤max{D_k,(r_1+r_2+…r_k)/k}其中D_k为矩阵A所有k阶主子阵之列和最大值,r_1≥r_2≥…≥r_n为从大到小排序的行和,所得结果易于计算且较经典的Frobienus界值精确.同时也得到一个类似下界.Some bounds for the Perron root p of irreducible nonnegative matrices are proposed. Let A be any nonnegative matrix, then for any k（1 ≤ k ≤ n）, we have ρ（A）≤max{Dk,（r1＋r2＋…rk）/k} where Dk is the maximum column-sum of all the k-th order principal submatrix of matrix A, and r1, r2,…, rk are the first k row-sums of A. At the same time, a similar lower bound is also proposed. These bounds are easy to compute and can be sharper than the classical Frobienus bounds.

关 键 词：PERRON根 非负不可约矩阵 上下界 

分 类 号：O151.21[理学—数学]