正则M-矩阵的平方根  

On the Square Root of Regular M-matrices

作　　者：关晋瑞 王志欣 李宣达 GUAN Jinrui;WANG Zhixin;LI Xuanda(School of Mathematics and Statistics,Taiyuan Normal University,Shanxi Jinzhong 030619,China;School of Science,Northeast University,Liaoning Shenyang 110819,China)

机构地区：[1]太原师范学院数学与统计学院,山西晋中030619 [2]东北大学理学院,辽宁沈阳110819

出　　处：《太原师范学院学报（自然科学版）》2023年第3期1-4,32,共5页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：国家自然科学基金(12001395);山西省科技创新人才团队专项资助(202204051002018);太原师范学院研究生教育创新项目(SYYJSYC-2314).

摘　　要：矩阵平方根在数学的许多领域中具有广泛的应用.文章利用M-矩阵的性质和二次矩阵方程理论,研究了正则M-矩阵的平方根,证明了正则M-矩阵的平方根总是存在的,而且该平方根仍是一个正则的M-矩阵.最后通过数值例子对本文的理论和方法进行了验证.The square root of matrix is widely used in many fields of mathematics.Based on the properties of M-matrix and quadratic matrix equation,we study the square root of regular M-matrices,and prove that the square root of a regular M-matrix exists,and is still a regular M-matrix.In addition,an iterative method is proposed to calculate the square root and the corresponding convergence analysis is given.Numerical examples are given to illustrate the theory and the method in this paper.

关 键 词：矩阵平方根 正则M-矩阵 迭代法 

分 类 号：O241.6[理学—计算数学]