| 矩阵方程AXB+CYD=E的双中心最小二乘问题 |
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| 引用本文： | 梁艳芳,袁仕芳.矩阵方程AXB+CYD=E的双中心最小二乘问题[J].五邑大学学报(自然科学版),2014(4):6-12. |
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| 作者姓名： | 梁艳芳 袁仕芳 |
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| 作者单位： | 五邑大学 数学与计算科学学院,广东 江门,529020 |
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| 基金项目： | 国家自然科学基金资助项目(11301397)；江门市科技攻关项目 |
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| 摘 要： | 利用矩阵的Kronecker积、列拉直算子和Moore-Penrose广义逆,讨论矩阵方程AXB+CYD=E的双中心最小二乘问题,得到双中心极小范数最小二乘解和对称双中心极小范数最小二乘解的表达式,给出求双中心极小范数最小二乘解的数值解法和数值例子.
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| 关 键 词： | 双中心矩阵 对称双中心矩阵 最小二乘解 极小范数解 Moore-Penrose广义逆 Kronecker积 |
Least Squares Double Center Problem of the Matrix Equation+ =AXB CYD E with the Least Norm |
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| LIANG Yan-fang,YUAN Shi-fang.Least Squares Double Center Problem of the Matrix Equation+ =AXB CYD E with the Least Norm[J].Journal of Wuyi University(Natural Science Edition),2014(4):6-12. |
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| Authors: | LIANG Yan-fang YUAN Shi-fang |
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| Institution: | (School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China) |
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| Abstract: | Given matrices of A∈R^m×n , B∈R^n×s , C∈Rm×k , D∈Rk×s ,E∈R^m×s using the Kronecker product, the Vec-operation and Moore-Penrose generalized inverse of matrices, we derive the expressions of the least squares double center solution with the least norm and the least squares symmetric double center solution with the least norm of the matrix equation ＋ =AXB CYD E . We also provide a numerical algorithm and numerical experiments for finding the least squares double center solution with the least norm. |
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| Keywords: | double center matrices symmetric double center matrices least-squares solutions least norm solutions Moore-Penrose generalized inverse the Kronecker product |
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