二次矩阵方程异类约束1-3-7解的迭代算法  

Iterative Algorithm for 1-3-7 Solutions of Quadratic Matrix Equation with Heterogeneous Constraints

作　　者：陈世军 余胜斌 Chen Shijun;Yu Shengbin(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：《宁夏大学学报（自然科学版）》2021年第3期251-256,共6页Journal of Ningxia University(Natural Science Edition)

基　　金：福建省教育厅中青年教师教育科研项目(JAT190410);2018年度福建省高等学校新世纪优秀人才支持计划;福建省自然科学基金资助项目(2019J01089)。

摘　　要：讨论了控制理论中二次矩阵方程的约束解问题,结合牛顿算法以及修正共轭梯度算法(MCG),建立了多变量二次矩阵方程异类约束1-3-7解的牛顿-MCG算法.先用牛顿算法把非线性二次矩阵方程转化为关于校正矩阵的线性矩阵方程,再用MCG算法求线性矩阵方程异类约束解或最小二乘约束解,给出了算法性质和结论.最后,用数值算例验证了该算法是有效的.The constrained solutions of quadratic matrix equations in control theory are discussed.Combined with Newton algorithm and modified conjugate gradient algorithm(MCG),a Newton-MCG algorithm is established to solve the 1-3-7 solutions of the multivariable quadratic matrix equations with heterogeneous constraints.Firstly,the nonlinear quadratic matrix is transformed into a linear matrix equation with respect to the correction matrix by Newton’s algorithm,and then the modified conjugate gradient algorithm is used to solve the heterogeneous constrained solution or least squares constrained solution of the linear matrix equation.The properties and convergence results of the algorithm are given.Numerical examples are given to verify the effectiveness of the algorithm.

关 键 词：二次矩阵方程 异类约束解 修正共轭梯度法 牛顿算法 

分 类 号：O241.6[理学—计算数学]