| 一类广义Sylvester方程的反对称最小二乘解及其最佳逼近 |
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| 引用本文： | 邓远北,胡锡炎.一类广义Sylvester方程的反对称最小二乘解及其最佳逼近[J].系统科学与数学,2004,24(3):382-388. |
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| 作者姓名： | 邓远北 胡锡炎 |
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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： | 国家自然科学基金资助课题 |
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| 摘 要： | 本文利用矩阵的奇异值分解(SVD),给出了广义Sylvester矩阵方程AX YA=C反对称解存在的充分必要条件,导出了其反对称解和反对称最小二乘解的表达式,同时在解集合中得到了对给定矩阵的最佳逼近解.
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| 关 键 词： | 矩阵方程 矩阵范数 反对称矩阵 最佳逼近 |
| 修稿时间： | 2002年1月10日 |
THE LEAST-SQUARES SKEW-SYMMETRIC SOLUTION AND THE OPTIMAL APPROXIMATION ON A CLASS OF GENERALIZED SYLVESTER EQUATION |
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| Yuan Bei DENG,Xi Yan HU.THE LEAST-SQUARES SKEW-SYMMETRIC SOLUTION AND THE OPTIMAL APPROXIMATION ON A CLASS OF GENERALIZED SYLVESTER EQUATION[J].Journal of Systems Science and Mathematical Sciences,2004,24(3):382-388. |
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| Authors: | Yuan Bei DENG Xi Yan HU |
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| Institution: | College of Mathematics and Econometrics,Hunan University, Changsha 410082 |
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| Abstract: | Using the singular value decomposition (SVD) of the matrix A, this paper obtains the necessary and sufficient conditions for the existence of and the expresssions of the skew-symmetric solutions of the generalized Sylvester matrix equation AX YA = C, and the least-squares skew-symmetric solution of this equation. In addition, in the solution set of the corresponding problems, the expressions of the optimal approximation solutions are derived for the given marices . |
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| Keywords: | Matrix equation matrix norm skew-symmetric matrix optimal approximation |
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