| 一类四元数矩阵方程的反Hermite极小范数最小二乘解 |
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| 引用本文： | 袁仕芳. 一类四元数矩阵方程的反Hermite极小范数最小二乘解[J]. 四川理工学院学报(自然科学版), 2009, 22(4): 25-28 |
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| 作者姓名： | 袁仕芳 |
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| 作者单位： | 五邑大学数学物理系,广东,江门,529020 |
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| 基金项目： | 广东省高校优秀青年创新人才培育项目 |
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| 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。
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| 关 键 词： | 四元数矩阵 矩阵方程 Moore-Penrose广义逆 Kronecker积 |
Least Squares Solution for a Kind of Quaternion Matrix Equation with the Least Norm |
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| YUAN Shi-fang. Least Squares Solution for a Kind of Quaternion Matrix Equation with the Least Norm[J]. Journal of Sichuan University of Science & Engineering(Natural Science Editton), 2009, 22(4): 25-28 |
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| Authors: | YUAN Shi-fang |
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| Affiliation: | Department of Mathematics and Physics;Wuyi University;Jiangmen 529020;China |
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| Abstract: | In this paper,by applying a new way of vec(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 f... |
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| Keywords: | quaternion matrices matrix equation Moore-Penrose generalized inverse Kronecker product |
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