| 一种求解复Hermite矩阵特征值的方法 |
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| 引用本文： | 李小波,薛王伟,孙志勇.一种求解复Hermite矩阵特征值的方法[J].数据采集与处理,2005,20(4):403-406. |
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| 作者姓名： | 李小波 薛王伟 孙志勇 |
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| 作者单位： | 1. 北京理工大学电子工程系,北京,100081
2. 解放军电子工程学院信息系,合肥,230037 |
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| 基金项目： | 国防科技重点实验室基金（00JS05.5.1JB3905）资助项目. |
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| 摘 要： | 介绍几种求解矩阵特征值和特征向量的经典算法及各自优缺点,通过理论推导,提出了一种性能稳健的方法,可以求解信号处理中常见的复Hermite阵.将对复Hermite矩阵求特征值和特征向量的问题转化为求解实对称阵的特征值和特征向量,而实对称阵的求解采用一种改进的三对角Householder法.最后把结果与Matlab仿真结果比较,可以看出该方法有很高的精确度.
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| 关 键 词： | Hermite矩阵 特征值 特征向量 实对称阵 Householder方法 |
| 文章编号： | 1004-9037（2005）04-0403-04 |
| 收稿时间： | 2004-12-27 |
| 修稿时间： | 2005-06-29 |
High Quality Method for Solving Eigenvalues of Complex Hermite Matrix |
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| LI Xiao-bo,XUE Wang-wei,SUN Zhi-yong.High Quality Method for Solving Eigenvalues of Complex Hermite Matrix[J].Journal of Data Acquisition & Processing,2005,20(4):403-406. |
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| Authors: | LI Xiao-bo XUE Wang-wei SUN Zhi-yong |
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| Affiliation: | 1. Department of Electronic Engineering, Beijing Institute of Technology, Beijing, 100081 ,China; 2. Department of Information, Electronic Engineering Institute of PLA, Hefei, 230037,China |
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| Abstract: | Several kinds of classic algorithms for solving eigenvalues and eigenvectors of the matrix are presented. Then by the theoretical deduction, a reliable method is used to solve a complex Hermite matrix in signal proceeding. The problems of eigenvalues and eigenvectors of the complex Hermite matrix can be tranformed to evaluate a real symmetric ones of the matrix. The improved Householder method is used to calculate the real symmetric matrix. Finally, compared with the Matlab result, the method has a high precision. |
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| Keywords: | Hermite matrix eigenvalue eigenvector real symmetric matrix Householder method |
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