| 矩阵方程AXB+CY D=E的三对角中心对称极小范数最小二乘解 |
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| 引用本文： | 彭雪梅,张爱华,张志强. 矩阵方程AXB+CY D=E的三对角中心对称极小范数最小二乘解[J]. 数学杂志, 2014, 34(6): 1163-1169 |
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| 作者姓名： | 彭雪梅 张爱华 张志强 |
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| 作者单位： | 武汉东湖学院基础课部;军事经济学院基础部;武昌工学院信息工程学院; |
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| 摘 要： | 本文研究了矩阵方程AXB+CY D=E的三对角中心对称极小范数最小二乘解问题.利用矩阵的Kronecker积和Moore-Penrose广义逆方法,得到了矩阵方程AXB+CY D=E的三对角中心对称极小范数最小二乘解的表达式.
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| 关 键 词： | 三对角中心对称矩阵 极小范数解 最小二乘解 Moore-Penrose广义逆 Kronecker积 |
| 收稿时间： | 2014-01-22 |
| 修稿时间： | 2014-06-23 |
CENTROSYMMETRIC TRIDIAGONAL LEAST SQUARES SOLUTION OF THE MATRIX EQUATION AXB + CYD = E WITH THE LEAST NORM |
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| PENG Xue-mei,ZHANG Ai-hua and ZHANG Zhi-qiang. CENTROSYMMETRIC TRIDIAGONAL LEAST SQUARES SOLUTION OF THE MATRIX EQUATION AXB + CYD = E WITH THE LEAST NORM[J]. Journal of Mathematics, 2014, 34(6): 1163-1169 |
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| Authors: | PENG Xue-mei ZHANG Ai-hua ZHANG Zhi-qiang |
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| Affiliation: | Department of Basic Courses, Wuhan Donghu University, Wuhan 430212, China,Department of Basic Courses, Army Military Economics Institute, Wuhan 430035, China and College of Information Engineering, Wuchang Institute of Technology, Wuhan 430065, China |
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| Abstract: | In this paper, we investigate the centrosymmetric tridiagonal least squares solution of the matrix equation with the least norm. By the means of Moore-Penrose generalized inverse and Kronecker product, we obtain the expression of the centrosymmetric tridiagonal least squares solution of the matrix equation AXB + CYD = E with the least norm. |
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| Keywords: | centrosymmetric tridiagonal matrix least norm solution least squares solution Moore-Penrose generalized inverse the Kronecker product |
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