| 关于矩阵方程AXB=E的加权最小二乘Hermite解 |
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| 引用本文： | 王明辉,魏木生.关于矩阵方程AXB=E的加权最小二乘Hermite解[J].计算数学,2004,26(2):129-136. |
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| 作者姓名： | 王明辉 魏木生 |
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| 作者单位： | 1. 华东师范大学数学系,上海,200062；曲阜师范大学数学系,山东,273165
2. 华东师范大学数学系,上海,200062 |
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| 基金项目： | 国家自然科学基金(编号: 10371044)，上海重点学科科研基金资助项目. |
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| 摘 要： | In this paper, we discuss the matrix equation AXB = C. We obtain a terse expression of weighted least-squares solution by applying the canonical correlation decomposition(CCD), we discuss the sufficient and necessary conditions for existence of Hermitian solutions, and derive a general form of the Hermite solutions.We also derive the expression of the optimal approximation solution in the set of Hermite soluti6ns to given matrix.
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| 关 键 词： | 标准相关分解 加权最小二乘解 最佳逼近解 矩阵方程 |
ON WEIGHTED LEAST-SQUARES HERMITE SOLUTION OF MATRIX EQUATION AXB = E |
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| Wang Minghui.ON WEIGHTED LEAST-SQUARES HERMITE SOLUTION OF MATRIX EQUATION AXB = E[J].Mathematica Numerica Sinica,2004,26(2):129-136. |
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| Authors: | Wang Minghui |
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| Institution: | Wang Minghui
(Department of Mathematics, East China Normal University, Shanghai, 200062; Department of Mathematics, Qufu Teacher's University, Shandong, 273165)
Wei Musheng (Department of Mathematics, East China Normal University, Shanghai, 200062) |
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| Abstract: | In this paper, we discuss the matrix equation AXB = C. We obtain a terse expression of weighted least-squares solution by applying the canonical correlation decomposition(CCD). we discuss the sufficient and necessary conditions for existence of Hermitian solutions, and derive a general form of the Hermite solutions. We also derive the expression of the optimal approximation solution in the set of Hermite solutions to given matrix. |
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| Keywords: | CGD weighted least squares optimal approximation |
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