一类求实对称正定矩阵逆的二次收敛算法  

A Class of Iteration Method for Computing the Inverse of Real Symmetric Positive Definite Matrices

作　　者：关晋瑞[1] 宋儒瑛[1] GUAN Jinrui;SONG Ruying(Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院数学系,山西晋中030619

出　　处：《忻州师范学院学报》2021年第2期7-9,17,共4页Journal of Xinzhou Teachers University

基　　金：山西省高等学校科技创新项目(2019L0783);山西省应用基础研究计划项目(201901D211423)。

摘　　要：文章研究了实对称正定矩阵逆的计算问题.首先将逆矩阵的计算转化为矩阵方程的求解,进而基于系数矩阵的分裂,提出了一类迭代法以计算逆矩阵.理论分析显示,适当选取参数后该迭代法是收敛的,且具有二次收敛率.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。In this paper,the inverse of real symmetric positive definite matrix is studied.First,the matrix inverse is converted into linear matrix equation,and then a kind of iteration method is proposed to compute the inverse matrix based on the splitting of coefficient matrix.Theoretical analysis shows that the new method is convergent with proper parameters and has a quadratic convergence rate.Numerical experiments show that the new method is feasible and effective under certain conditions.

关 键 词：实对称正定矩阵 逆矩阵 迭代法 二次收敛率 

分 类 号：O241.6[理学—计算数学] O151.21[理学—数学]