四元数矩阵方程(AXB,CXD)=(E,F)的最小范数最小二乘Hermitian解  

The minimal norm least squares Hermitian solution of the quaternion matrix equation(AXB,CXD)=(E, F)

作　　者：王秀平 张凤霞[2] Wang Xiuping;Zhang Fengxia(Schoolof of Pharmacy,Liaocheng University,Liaocheng 252059,China;School of Mathematics Science,Liaocheng University,Liaocheng 252059,China)

机构地区：[1]聊城大学药学院,山东聊城252059 [2]聊城大学数学科学学院,山东聊城252059

出　　处：《纯粹数学与应用数学》2020年第1期105-118,共14页Pure and Applied Mathematics

基　　金：山东省自然科学基金(ZR2018MF020);山东省教育厅科研发展计划项目(J15LI10);聊城大学科技计划项目(318011318).

摘　　要：提出了研究四元数矩阵方程(AXB, CXD)=(E, F)的最小范数最小二乘Hermitian解的一个有效方法.首先应用四元数矩阵的实表示矩阵以及实表示矩阵的特殊结构,把四元数矩阵方程转化为相应的实矩阵方程,然后求出四元数矩阵方程(AXB, CXD)=(E, F)的最小二乘Hermitian解集,进而得到其最小范数最小二乘Hermitian解.所得到的结果只涉及实矩阵,相应的算法只涉及实运算,因此非常有效.最后的两个数值例子也说明了这一点.In this paper, we propose an efficient method for the minimal norm least squares Hermitian solution of the quaternion matrix equation(AXB, CXD) =(E, F). By using the real representation matrices of quaternion matrices, the particular structure of the real representation matrices, wefirst convert the quaternion matrix equation into the corresponding real matrix equation. Then, we solve the least squares Hermitian solution set of the quaternion matrix equation(AXB, CXD) =(E, F),and furthermore we obtain its minimal norm least squares Hermitian solution. Our results only involve real matrices, and the corresponding algorithm only involves real arithmetic. Therefore, they are very effective. The final two numerical examples also illustrate the effectiveness of our method.

关 键 词：四元数矩阵方程 最小二乘Hermitian解 实表示矩阵 

分 类 号：O151.21[理学—数学]