一类计算M-矩阵平方根的二次收敛算法  

A CLASS OF QUADRATIC CONVERGENCE ALGORITHM FOR CALCULATING THE SQUARE ROOT OF M-MATRIX

作　　者：关晋瑞[1] 邵荣侠 任孚鲛[1] Guan Jinrui;Shao Rongxia;Ren Fujiao(Department of Mathematics,Taiyuan Normal University,Jinzhong 030619;School of Statistics and Data Science,Xinjiang University of Finance and Economics,Urumqi 830012)

机构地区：[1]太原师范学院数学系,晋中030619 [2]新疆财经大学统计与数据科学学院,新疆830012

出　　处：《南京大学学报（数学半年刊）》2022年第2期155-165,共11页Journal of Nanjing University(Mathematical Biquarterly)

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)。

摘　　要：矩阵的平方根广泛出现在科学计算和工程应用的很多领域中,本文研究了M-矩阵平方根的数值算法.基于一类简单的位移变换,将M-矩阵平方根的计算转化为M-矩阵代数Riccati方程的求解,并提出了一类迭代法以计算M-矩阵代数Riccati方程.理论分析显示,新方法具有二次收敛率.数值实验表明,新方法是可行的,而且在一定情况下也是较为有效的.The square root of matrix is widely used in many fields of scientific calculation and engineering application.In this paper,the numerical algorithm for the square root of M-matrix is studied.Based on a kind of simple displacement transformation,the square root of M-matrix is transformed into the solution of M-matrix algebraic Riccati equation.A class of iterative method is proposed to calculate the M-matrix algebraic Riccati equation.Theoretical analysis shows that the new method has quadratic convergence rate.Numerical experiments show that the new method is feasible and effective in some cases.

关 键 词：矩阵平方根 M-矩阵 M-矩阵代数Riccati方程 迭代法 

分 类 号：O241.6[理学—计算数学]