| 矩阵广义奇异值分解的一个新证法及推论 |
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| 引用本文： | 孟纯军,胡锡炎.矩阵广义奇异值分解的一个新证法及推论[J].湖南大学学报(自然科学版),2007,34(5):87-89. |
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| 作者姓名： | 孟纯军 胡锡炎 |
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| 作者单位： | 湖南大学,数学与计量经济学院,湖南,长沙,410082 |
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| 基金项目： | 国家自然科学基金资助项目(10571047)，博士后基金资助项目(20060390888) |
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| 摘 要： | 从矩阵对的CS分解理论出发,给出了广义奇异值分解的一个新的证明.给出了关于矩阵对广义奇异值的三个有用的推论.最后给出了计算矩阵对的广义奇异值分解的一个算法.数值实例说明算法是可行且有效的.
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| 关 键 词： | 广义奇异值分解(GSVD) CS分解 算法 |
| 文章编号： | 1000-2472（2007）05-0087-03 |
| 修稿时间： | 2006-06-15 |
A New Proof of Generalized Singular-Value Decomposition |
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| MENG Chun-jun,HU Xi-yan.A New Proof of Generalized Singular-Value Decomposition[J].Journal of Hunan University(Naturnal Science),2007,34(5):87-89. |
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| Authors: | MENG Chun-jun HU Xi-yan |
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| Institution: | College of Mathematics and Econometrics,Hunan Univ,Changsha,Hunan 410082,China |
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| Abstract: | The generalized singular-value decomposition of the matrix pair A and B this a powerful tool for solving the constrained matrix equations.With the aid of the CS decomposition of the matrix pair A and B,this paper gave a new proof of the theorem of the generalized singular-value decomposition of the matrix pair A and B.Three useful corollaries on the generalized singular-values of the matrix pair were presented.Finally,an algorithm was also provided to compute the generalized singular-value decomposition of the matrix pairs A and B.Some examples were given to show that the algorithm was both feasible and efficient. |
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| Keywords: | generalized singular-value decomposition(GSVD) CS decomposition algorithm |
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