| 双中心矩阵反问题及其在电网络理论中的应用 |
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| 引用本文： | 周硕,吴柏生. 双中心矩阵反问题及其在电网络理论中的应用[J]. 工程数学学报, 2007, 24(4): 611-617 |
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| 作者姓名： | 周硕 吴柏生 |
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| 作者单位： | 东北电力大学理学院,吉林,132012;吉林大学数学研究所,长春,130012;吉林大学数学研究所,长春,130012 |
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| 基金项目： | 国家自然科学基金 , 高等学校博士学科点专项科研项目 |
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| 摘 要： | 本文研究双中心矩阵反问题。建立了双中心矩阵反问题的最小二乘解,得到了解的具体表达式。讨论了用双中心矩阵反问题的解构造给定矩阵的最佳逼近问题,给出该问题有解的充分必要条件和解的表达式。设计了相应的算法并给出了其在电网络理论中的应用。
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| 关 键 词： | 双中心矩阵 反问题 最佳逼近 电网络理论 |
| 文章编号： | 1005-3085（2007）04-0611-07 |
| 修稿时间： | 2005-05-09 |
The Inverse Problem of Doubly Center Matrices and Its Application to the Theory of Electric Network |
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| ZHOU Shuo,WU Bai-sheng. The Inverse Problem of Doubly Center Matrices and Its Application to the Theory of Electric Network[J]. Chinese Journal of Engineering Mathematics, 2007, 24(4): 611-617 |
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| Authors: | ZHOU Shuo WU Bai-sheng |
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| Affiliation: | 1. College of Science, Northeast Dianli University, Jilin 132012; 2. Institute of Mathematics, Jilin University, Changchun 130012 |
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| Abstract: | This paper is focused on the inverse problem of doubly center matrices. The least-square solutions to the inverse problem are established and their general form is given. Based on the solution set, the optimal approximation to a given matrix is constructed, and the necessary and sufficient conditions for the solvability of the problem are given and the expression for the solution is provided. The corresponding algorithms are proposed and applications to the theory of electric network are illustrated by examples. |
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| Keywords: | doubly center matrices inverse problem optimal approximation theory of electric network |
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