约束矩阵方程的Hermitian解的共轭梯度迭代算法  

A Conjugate Gradient Iterative Algorithm for Hermitian Solutions of Matrix Equations with Constraints

作　　者：岳潇荣 周富照[1] 

机构地区：[1]长沙理工大学数学与统计学院,长沙410114

出　　处：《数学理论与应用》2016年第4期23-28,共6页Mathematical Theory and Applications

基　　金：国家自然科学基金资助项目(11371072)

摘　　要：本文讨论矩阵方程在子矩阵约束下的Hermitian解的共轭梯度迭代算法,先转化成两个低阶方程,然后利用共轭梯度思想分别构造出低阶方程的共轭梯度迭代算法,运用算法求出矩阵方程的Hermitian解及最佳逼近,最后给出了数值实例来验证算法的有效性.In this paper, we give a conjugate gradient iterative algorithm for Hermitian solutions of matrix equations under submatrix constraints. First, we transform the equations into two lower--order equations, then we construct a gradient iterative algorithm by conjugate gradients for lower--order equations to obtain the solutions and the optimal approximation of the matrix equations. Finally some numerical examples are given to verify the effectiveness of this method.

关 键 词：子矩阵约束 Hermitian解 共轭梯度迭代法 最佳逼近解 

分 类 号：O241.6[理学—计算数学]