M-矩阵Hadamard积最小特征值下界的改进  

A Modification on the Minimum Eigenvalue’s Bounds of the Hadamard Product of M-Matrices

作　　者：周平[1] ZHOU Ping(School of Artificial Intelligence,Wenshan University,Wenshan Yunnan 663099,China)

机构地区：[1]文山学院人工智能学院,云南文山663099

出　　处：《文山学院学报》2024年第5期54-57,共4页Journal of Wenshan University

基　　金：云南省教育厅科研基金项目“几类结构矩阵的Schur补及其相关问题研究”(2022J0949)。

摘　　要：针对非奇异M-矩阵和M-矩阵的逆矩阵Hadamard积的最小特征值下界问题,结合M-矩阵的逆矩阵元素的上界、特征值包含域定理以及不等式放缩技巧,获得两个容易计算的、具有可调节参数且只与矩阵元素相关的新估计式,同时给出当A-1是双随机矩阵时的两个改进的估计式,并通过理论分析和数值例子对比表明新下界比已有的结果更精确,具有一定的优越性和有效性。In this paper,the minimum lower bound of eigenvalues for the Hadamard product of non-singular M-matrix and the inverse matrix of M-matrix are discussed,two new estimators are obtained,which are easy to calculate,have adjustable parameters and are only related to matrix elements.And two improved estimators are given when A-1is doubly stochastic matrix.It is shown that the new lower bounds are more accurate than some other conclusions through theoretical analysis and numerical examples,and has some advantages and effectiveness.

关 键 词：M-矩阵 HADAMARD积 双随机矩阵 最小特征值 新下界 

分 类 号：O151.21[理学—数学]