严格对角占优M-矩阵的逆矩阵的无穷大范数的上界估计  

Estimation on Upper Bounds for the Infinity Norms of Inverses Matrix of Strictly Diagonally Dominant M-matrices

作　　者：赵仁庆 甘小艇 张坤 ZHAO Ren-qing;GAN Xiao-ting;ZHANG Kun(School of Mathematics and Statistics,Chuxiong Normal University,Chuxiong,Yunnan 675000)

机构地区：[1]楚雄师范学院数学与统计学院,云南楚雄675000

出　　处：《工程数学学报》2021年第2期249-256,共8页Chinese Journal of Engineering Mathematics

基　　金：云南省科技计划青年项目(2017FD149).

摘　　要：M-矩阵是应用背景很广的一类特殊矩阵,生物学、物理学和社会科学等方面的许多问题都与M-矩阵有着密切的联系,因此对M-矩阵的研究具有重要意义.本文首先引入一组新的记号,给出严格对角占优M-矩阵及其逆矩阵元素关系的两个不等式,由此得到了逆矩阵的无穷大范数上界估计式,最后给出矩阵A的最小特征值的下界,这些估计式只依赖于矩阵A的元素.理论分析和数值算例表明新估计式改进了相关结果.M-matrix is a kind of special matrix which has wide applications.Many problems in biology,physics and social science and so on have close connection with M-matrice,hence researches on M-matrix is valuable.In this paper,firstly,some new notations are introduced,and two inequalities of element relation on strictly diagonally dominant M-matrix and the inverse matrix are given.Secondly,some new upper bounds for the infinity norm of inverse matrix are obtained.Finally,the lower bound of the smallest eigenvalue of matrix A is presented,which only depends on the elements of matrix A.The theoreical analysis and numerical examples show that the new upper bounds improve the related results.

关 键 词：对角占优矩阵 M-矩阵 无穷大范数 上界 最小特征值 

分 类 号：O151.21[理学—数学]