广义约束条件下矩阵方程AXB+CX^(T)D=E最佳逼近解的迭代算法  

Iterative Algorithm for the Optimal Approximation Solution of Matrix Equations AXB+CX^(T)D=E with Generalized Constraint

作　　者：杨家稳[1] 万鹏 梁金荣[1] YANG Jiawen;WAN Peng;LIANG Jinrong(Department of Basic Course,Chuzhou Polytechnic,Chuzhou 239000,Anhui China)

机构地区：[1]滁州职业技术学院基础教学部,安徽滁州239000

出　　处：《吉首大学学报(自然科学版)》2025年第1期1-11,共11页Journal of Jishou University(Natural Sciences Edition)

基　　金：安徽省高校自然科学重点项目基金(2023AH053087,KJ2018A0839)。

摘　　要：为了计算广义约束条件GX=H下矩阵方程AXB+CX^(T)D=E的最佳逼近解,设计了一种基于梯度投影与搜索方向正交的迭代算法.证明了任意给定一个满足广义约束条件的特殊初始矩阵,通过有限次迭代算法,能够获得广义约束条件下矩阵方程的极小范数最小二乘解,并利用该极小范数最小二乘解计算出最佳逼近解.An iterative algorithm is presented to calculate the optimal approximation solution of the matrix equations AXB+CX^(T)D=E with constraint conditions GX=H.It is proved that given a special initial matrix satisfying the generalized constraints,the minimal norm least squares solution of the matrix equation under the generalized constraints can be obtained by the finite-order iterative algorithm,and the optimal approximation solution can be calculated by using the minimal norm least squares solution.

关 键 词：极小范数最小二乘解 最佳逼近解 迭代算法 梯度投影 

分 类 号：O24[理学—计算数学]