矩阵方程AXB = C的轮换极小范数最小二乘解  

Least Squares Circulant Solution of the Matrix Eqaution AXB = C with the Least Norm

作　　者：曹煜喆 袁仕芳[1] 

机构地区：[1]五邑大学数学与计算科学学院,广东江门

出　　处：《理论数学》2022年第8期1360-1369,共10页Pure Mathematics

摘　　要：循环矩阵有悠久的历史并且在众多科学领域得到了广泛的应用。矩阵方程AXB=C在特定集合类的求解和最小化问题在工程等领域有重要的应用。本文通过矩阵的Kronecker积和Moore-Penrose广义逆得到了矩阵方程AXB=C有轮换解的充要条件和解的表达式。在没有轮换解时,给出了方程的轮换极小范数最小二乘解。在论文末节,给出方程求解的数值算法与数值例子。Circulant matrices have been around for a long time and have been extensively used inmany scientific areas. The problem of solving and minimizing the matrix AXB = C in a specific set class has important applications in engineering and other related fields. In this paper, by using Kronecker product and Moore-Penrose generalized inverse of the matrices, the necessary and suficient conditions for AXB = C having circulant solution are obtained. We derive the expression of the least squares circulant solution of the matrix equation AXB = C with the least norm when there is no circulant solution. In the last section, the numerical algorithm and numerical examples are also given.

关 键 词：轮换矩阵 极小范数解 最小二乘解 MOORE-PENROSE广义逆 Kronecker 积 

分 类 号：O151.21[理学—数学]