| 矩阵方程ATXA=B的对称正交对称解及其最佳逼近 |
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| 引用本文： | 彭亚新,胡锡炎,张磊.矩阵方程ATXA=B的对称正交对称解及其最佳逼近[J].高等学校计算数学学报,2003,25(4):372-377. |
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| 作者姓名： | 彭亚新 胡锡炎 张磊 |
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| 作者单位： | 湖南大学数学与计量经济学院,长沙,410082 |
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| 基金项目： | 国家自然科学基金(10171031) |
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| 摘 要： | By applying the generalized singular value decomposition of matrices, this paper provides the necessary and sufficient conditions for the existence and the expression of the symmetric ortho-symmetric solutions of the linear matrix equation A^TXA = B. In addition, the expression of the optimal approximation solution to the given matrix is derived.
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| 关 键 词： | 矩阵方程 对称正交对称解 奇异值 通解公式 |
| 修稿时间： | 2002年9月29日 |
THE SYMMETRIC ORTHO-SYMMETRIC SOLUTION OF LINEAR MATRIX EQUATION ATXA= B AND ITS OPTIMAL APPROXIMATION |
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| Peng Yaxin Hu Xiyan Zhang Lei.THE SYMMETRIC ORTHO-SYMMETRIC SOLUTION OF LINEAR MATRIX EQUATION ATXA= B AND ITS OPTIMAL APPROXIMATION[J].Numerical Mathematics A Journal of Chinese Universities,2003,25(4):372-377. |
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| Authors: | Peng Yaxin Hu Xiyan Zhang Lei |
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| Abstract: | By applying the generalized singular value decomposition of matrices, this paper provides the necessary and sufficient conditions for the existence and the expression of the symmetric ortho-symmetric solutions of the linear matrix equation ATXA=B. In addition, the expression of the optimal approximation solution to the given matrix is derived. |
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| Keywords: | matrix equation symmetric ortho-symmetric matrices matrix norm optimal approximation |
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