| 二次特征值反问题的对称次反对称解及其最佳逼近 |
| |
| 引用本文： | 郭丽杰,周硕.二次特征值反问题的对称次反对称解及其最佳逼近[J].吉林大学学报(理学版),2009,47(6):1185-1190. |
| |
| 作者姓名： | 郭丽杰 周硕 |
| |
| 作者单位： | 东北电力大学 理学院, 吉林 吉林 132012 |
| |
| 基金项目： | 吉林省科技发展计划项目基金 |
| |
| 摘 要： | 利用矩阵的奇异值分解和矩阵的Kronecker乘积, 讨论构造对称次反对称矩阵M,C和K, 使得二次约束Q(λ)=λ2M+λC+K具有给定特征值和特征向量的特征值反问题. 首先证明反问题是可解的, 并给出了解集SMCK的通式. 进而考虑了解集SMCK中对给定矩阵的最佳逼近问题, 得到了最佳逼近解.
|
| 关 键 词： | 二次特征值 对称次反对称矩阵 反问题 最佳逼近 奇异值分解 |
| 收稿时间： | 2009-02-19 |
Symmetric and Skew Anti-symmetric Solution of Inverse Quadratic Eigenvalue Problem and Its Optimal Approximation |
| |
| GUO Li-jie,ZHOU Shuo.Symmetric and Skew Anti-symmetric Solution of Inverse Quadratic Eigenvalue Problem and Its Optimal Approximation[J].Journal of Jilin University: Sci Ed,2009,47(6):1185-1190. |
| |
| Authors: | GUO Li-jie ZHOU Shuo |
| |
| Institution: | College of Science, Northeast Dianli University, Jilin 132012, Jilin Province, China |
| |
| Abstract: | The inverse eigenvalue problem of constructing symmetric and skew anti-symmetric matrices M,C and K of size n for the quadratic pencil Q(λ) = λ~2M + λC + K so that Q(λ) has a prescribed subset of eigenvalues and eigenvectors was considered by means of singular value decomposition of matrix and Kronecker product of matrices. The problem was firstly improved to be solvable and the general expression of the solution to the problem was provided. The optimal approximation problem associated with S_(MCK) was posed, that is, to find the nearest triple matrix ((M),(C),(K)) from S_(MCK). The existence and uniqueness of the optimal approximation problem was discussed and the exoression was provided for the optimal approximation problem. |
| |
| Keywords: | quadratic eigenvalue problem symmetric and skew anti-symmetric matrix inverse problem optimal approximation singular value decomposition |
| 本文献已被 万方数据 等数据库收录！ |
| 点击此处可从《吉林大学学报(理学版)》浏览原始摘要信息 |
| 点击此处可从《吉林大学学报(理学版)》下载免费的PDF全文 |
|
