非负不可约矩阵最大特征值的估计法  

Estimation for Greatest Eigenvalues of Nonnegative Irreducible Matrices

作　　者：王芳芳 杨晋 WANG Fangfang YANG Jin(College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, Chin)

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《济南大学学报（自然科学版）》2017年第4期334-338,共5页Journal of University of Jinan(Science and Technology)

基　　金：山西省自然科学基金项目(2015011001)

摘　　要：为了估计非负不可约矩阵最大特征值的界,构造2个新矩阵,利用Perron-Frobenius定理和新构造矩阵的行和与列和的性质,估计非负不可约矩阵最大特征值的上、下界,并推导极限估计式。结果表明,这种基于PerronFrobenius定理的估计非负不可约矩阵最大特征值的方法的估计范围比已有结论更精确。To compute bounds for the greatest eigenvalue of nonnegative irreducible matrices, two matrices were constructed. The upper and lower bounds for the greatest eigenvalue of nonnegative irreducible matrices were estimated by using Perron-Frobenius theory and sums of rows and columns of constructed matrices. A limit estimation formula was deduced. The results show that the estimated value of the method of estimating the greatest eigenvalue of nonnegative irreducible matrices based on Perron-Frobenius theory is more accurate than the existing conclusion.

关 键 词：非负不可约矩阵 最大特征值 估计 

分 类 号：O151.21[理学—数学]