| 矩阵方程AXB=D的最小二乘Hermite解及其加权最佳逼近 |
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| 引用本文： | 姚国柱,廖安平.矩阵方程AXB=D的最小二乘Hermite解及其加权最佳逼近[J].数学理论与应用,2003,23(3):77-81. |
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| 作者姓名： | 姚国柱 廖安平 |
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| 作者单位： | [1]湖南师范大学数学与计算机科学学院，长沙,410081 [2]湖南大学数学与计量经济学院,长沙,410082 |
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| 摘 要： | 本中,我们讨论了矩阵方程AXB=D的最小二乘Hermite解,通过运用广义奇异值分解(GSVD)，获得了解的通式。此外,对于给定矩阵F，也得到了它的加权最佳逼近表达式。
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| 关 键 词： | 矩阵方程 最小二乘Hermite解 加权最佳逼近 广义奇异值分解 |
LEAST-SQUARES SOLUTION OF AXB=D OVER HERMITIAN MATRICES X AND WEIGHTED OPTIMAL APPROXIMATION |
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| Yao Guozhu.LEAST-SQUARES SOLUTION OF AXB=D OVER HERMITIAN MATRICES X AND WEIGHTED OPTIMAL APPROXIMATION[J].Mathematical Theory and Applications,2003,23(3):77-81. |
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| Authors: | Yao Guozhu |
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| Abstract: | In this paper,we consider least-squares solution of AXB=D with respect to Hermitian matrix X.By applying the generalized singular value decomposition(GSVD),we obtain the general formulas of the solution.In addition,the expression of the weighted optimal approximation for given matrix F is also derived. |
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| Keywords: | Least-squares solution Generalized singular value decomposition Weighted optimal approximation |
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