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 for strictly diagonally dominant M-matrices

作　　者：赵仁庆[1] 郑伟 李云奎 ZHAO Ren-qing;ZHENG Wei;LI Yun-kui(School of Mathematics and Computer Science,Chuxiong Normal University,Chuxiong,Yunnan,675000;School of Education,Chuxiong Normal University,Chuxiong,Yunnan,675000)

机构地区：[1]楚雄师范学院数学与计算机科学学院,云南楚雄675000 [2]楚雄师范学院教育学院,云南楚雄675000

出　　处：《贵州师范学院学报》2021年第9期16-20,共5页Journal of Guizhou Education University

基　　金：云南省科技计划青年项目“H-矩阵的逆矩阵的无穷大范数上界和最小奇异值下界估计”(项目编号:2017FD149)。

摘　　要：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不等式,得到了逆矩阵的无穷大范数的上界估计式。给出矩阵A最小特征值的下界,从理论上证明了新估计式改进了某些现有文献的结果,同时数值算例说明了新估计式更精确。Firstly,some new notations are introduced in this paper,and some inequalities of element relation on strictly diagonally dominant M-matrix and its inverse matrix are given,the new upper bound of the infinite norm of the inverse matrix are obtained.In addition,the lower bound of the smallest eigenvalue of matrix A is presented.It is proved theoretically that the new upper bounds improve some existing results,and numerical examples show that the new estimation is more accurate.

关 键 词：严格对角占优矩阵 M-矩阵 无穷大范数 上界 最小特征值 

分 类 号：O151.21[理学—数学]