| 矩阵方程AHXA=B的反自反解及其最佳逼近 |
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| 引用本文： | 王艾红. 矩阵方程AHXA=B的反自反解及其最佳逼近[J]. 长沙大学学报, 2005, 19(5) |
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| 作者姓名： | 王艾红 |
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| 作者单位： | 长沙大学,教务处,湖南,长沙,410003 |
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| 摘 要： | 利用广义奇异值分解定理,得到了矩阵方程AHXA=B的反自反解存在的一个充要条件,并获得了相应的通解表达式和最佳逼近解,最后获得了最小范数解
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| 关 键 词： | 矩阵方程 反自反解 最佳逼近解 |
The Anti-reflexive Solutions of Matrix Equation and the Optimal Approximation |
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| WANG Aihong. The Anti-reflexive Solutions of Matrix Equation and the Optimal Approximation[J]. Journal of Changsha University, 2005, 19(5) |
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| Authors: | WANG Aihong |
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| Abstract: | Applying the generalized singular value decomposition(GSVD) of matrix pair,this paper provides the necessary and sufficient conditions for the existence and the expression for the anti-reflexive solutions of the matrix equation A~HXA=B.In addition,in solution set,the expressions of the optimal approximation solution to the given matrix and of minimum norm solution are derived. |
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| Keywords: | matrix equation anti-reflexive solutions optimal approximation solution |
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