| 可对称(半)正定化矩阵反问题的解及其最佳逼近 |
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| 引用本文： | 邓远北,肖庆丰. 可对称(半)正定化矩阵反问题的解及其最佳逼近[J]. 工程数学学报, 2006, 23(6): 1113-1116 |
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| 作者姓名： | 邓远北 肖庆丰 |
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| 作者单位： | 1. 中国科学院数学与系统科学研究院计算数学与科学工程计算研究所,北京,100080;湖南大学数学与计量经济学院,长沙,410082
2. 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;中国博士后科学基金 |
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| 摘 要： | 本文给出了矩阵反问题AX=B具有可对称正定化解与可对称半正定化解的必要充分条件,得到了通解的表达式,同时解决了方程的对称半正定化解对己给矩阵的最佳逼近问题。
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| 关 键 词： | 矩阵方程 矩阵范数 可对称(半)正定化矩阵 最佳逼近 |
| 文章编号： | 1005-3085(2006)06-1113-04 |
| 收稿时间： | 2004-12-13 |
| 修稿时间： | 2004-12-13 |
Solutions of Inverse Problems for Positive Definite (Semidefinite) Symmetrizable Matrices and the Optimal Approximation Problem |
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| DENG Yuan-bei,XIAO Qing-feng. Solutions of Inverse Problems for Positive Definite (Semidefinite) Symmetrizable Matrices and the Optimal Approximation Problem[J]. Chinese Journal of Engineering Mathematics, 2006, 23(6): 1113-1116 |
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| Authors: | DENG Yuan-bei XIAO Qing-feng |
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| Affiliation: | 1- Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080; 2- College of Mathematics and Econometrics, Hunan University, Changsha 410082 |
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| Abstract: | In this paper,the necessary and sufficient conditions for the existence of and the express- sions for the positive definite (semidefinite) symmetrizable solutions of inverse problems AX=B are obtained,and the optimal approximation semidefinite symmetrizable solution to given marices is also derived. |
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| Keywords: | matrix equation matrix norm positive definite symmetrizable matrices and semidefinite symmetrizab|e matrices optimal approximation |
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