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.
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)
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).
关键词
矩阵平方根
正则M-矩阵
迭代法
square root of matrix
regular M-matrix
iterative method
