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.
作者
杨家稳
万鹏
梁金荣
YANG Jiawen;WAN Peng;LIANG Jinrong(Department of Basic Course,Chuzhou Polytechnic,Chuzhou 239000,Anhui China)
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)。
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
minimal norm least squares solution
optimal approximation solution
iterative algorithm
gradient projection
