M-矩阵最小特征值下界的新不等式  

New Inequalities on the Lower Bounds for the Minimum Eigenvalue of M-matrix

作　　者：陈付彬[1] CHEN Fu-bin(Science Department,Kunming University of Science and Technology Oxbridge College,Kunming 650106,China)

机构地区：[1]昆明理工大学津桥学院理学部,云南昆明650106

出　　处：《数学的实践与认识》2020年第13期306-312,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11501141);云南省教育厅科学研究基金项目(2018JS747)。

摘　　要：非奇异M-矩阵B的最小特征值τ(B)的下界是矩阵论中重要的研究课题.利用特征值定位定理,首先给出非负矩阵与M-矩阵的逆矩阵Hadamard积的谱半径上界,进而给出M-矩阵最小特征值下界的新不等式.新不等式只与矩阵的元素有关,易于计算.理论分析和数值例子表明所给结果改进了现有结果.Lower bound on the minimum eigenvalue τ(B) of a nonsingular M-matrix B is an important research projects in the matrices theories.First,upper bounds for the spectral radius of the Hadamard product of a nonnegative matrix and the inverse matrix of a nonsingular M-matrix are given by using the location theorem of eigenvalue,furthermore new inequalities of the lower bounds for the minimum eigenvalue of M-matrix are given.The new inequalities only depend on the entries of matrix and they are easy to calculate.Theoretical analysis and numerical example show that the new results improve some existing results.

关 键 词：M-矩阵 谱半径 最小特征值 下界 

分 类 号：O151.21[理学—数学]