实方阵的Moore-Penrose对称{1,3}逆的MCG算法  

MCG Algorithm for Moore-Penrose Symmetric{1,3}Inverse of Real Matrix

作　　者：陈世军 CHEN Shi-jun(Department of Basic Teaching and Research,Yango University,Fuzhou 350015,China)

机构地区：[1]阳光学院基础教研部,福建福州350015

出　　处：《长春师范大学学报》2021年第6期1-5,共5页Journal of Changchun Normal University

基　　金：2019年福建省教育厅中青年教师教育科研项目“非线性矩阵方程子矩阵约束下对称解的双迭代算法研究”(JAT190410)。

摘　　要：讨论了广泛运用于控制理论、系统识别等领域的广义逆矩阵问题,借助求线性矩阵方程组的修正共轭梯度算法(MCG算法),提出求方阵对称{1,3}逆的修正共轭梯度算法,并证明了算法的收敛性。数值算例表明,该算法具有很高的计算效率。This paper discusses the generalized inverse matrix problem which is widely used in control theory,system identification and other fields.With the help of the modified conjugate gradient algorithm for solving linear matrix equations,a modified conjugate gradient algorithm for symmetric{1,3}inverse of square matrix is proposed.The convergence of the algorithm is proved.Numerical examples show that the algorithm has high computational efficiency.

关 键 词：广义逆 对称解 修正共轭梯度算法 Moore-Penrose 

分 类 号：O241.6[理学—计算数学]