一类四元数矩阵方程的反Hermite极小范数最小二乘解  

Least Squares Solution for a Kind of Quaternion Matrix Equation with the Least Norm

作　　者：袁仕芳[1] 

机构地区：[1]五邑大学数学物理系,广东江门529020

出　　处：《四川理工学院学报（自然科学版）》2009年第4期25-28,共4页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：广东省高校优秀青年创新人才培育项目(LYM08097)

摘　　要：利用文[Yuan S F,Liao A P,Lei Y.Least squares Hermitian solution of the matrix equation(AXB,CXD)=(E,F)with the least norm over the skew field of quaternions.Mathematical and ComputerModelling,2008,48:91-100]给出四元数矩阵A,B,C积的列拉直vec(ABC)的一种新方法和Moore-Penrose广义逆,研究四元数矩阵方程(AXB,CXD)=(E,F)的反Hermite极小范数最小二乘解,给出了它的通解表达式和求这个极小范数最小二乘解的数值算法。In this paper, by applying a new way ofvec（ABC） presented by Yuan et al. [ Yuan S F, Liao A P, Lei Y. Least squares Hermitian solution of the matrix equation （AXB, CXD） = （ E, F） with the least norm over the skew field of quaternions. Mathematical and Computer Modelling, 2008, 48：91-100 ], Moore-Penrose generalized inverse and Kronecker product of matrices, this paper derives the expressions of least squares anti-Hermitian solution of the quaternion matrix equation （ AXB, CXD） = （ E, F） with the least norm. Numerical algorithm for finding the least norm of least squares anti-Hermitian solution is also provided.

关 键 词：四元数矩阵 矩阵方程 Moore—Penrose广义逆 KRONECKER积 

分 类 号：O241.6[理学—计算数学]