|
|||||
|
|
| 埃尔米特自反矩阵的广义逆特征值问题与最佳逼近问题 | |
| 引用本文： | 王江涛,张忠志,谢冬秀,雷秀仁. 埃尔米特自反矩阵的广义逆特征值问题与最佳逼近问题[J]. 数值计算与计算机应用, 2010, 31(3): 232-240 |
| 作者姓名： | 王江涛 张忠志 谢冬秀 雷秀仁 |
| 作者单位： | 1. 华南理工大学理学院,广州,510640;华南理工大学工商管理学院,广州,510640 2. 东莞理工学院数学系,广东,东莞,523808 3. 北京信息科技大学理学院,北京,100192 4. 华南理工大学理学院,广州,510640 |
| 基金项目： | 国家自然科学基金，北京市教学名师建设项目 |
| 摘 要： | 在振动控制中,通常用矩阵的逼近问题来校正刚度矩阵和质量矩阵,使得它们具有给定的谱约束条件.本文基于埃尔米特自反矩阵的表示定理,利用矩阵的拉直和Kronecker积,得到了埃尔米特自反矩阵广义逆特征值问题解的一般表达式.进一步,对任意给定的n阶复矩阵对,利用Moor-Penrose广义逆和逼近理论,得到了其相关最佳逼近问题解的表达式. |
| 关 键 词： | 埃尔米特自反矩阵 广义特征值 矩阵拉直 最佳逼近 |
THE INVERSE GENERALIZED EIGENVALUE PROBLEM AND THE OPTIMAL APPROXIMATION FOR HERMITIAN-REFLEXIVE MATRICES |
|
| Wang Jiangtao,Zhang Zhongzhi,Xie Dongxiu,Lei Xiuren. THE INVERSE GENERALIZED EIGENVALUE PROBLEM AND THE OPTIMAL APPROXIMATION FOR HERMITIAN-REFLEXIVE MATRICES[J]. Journal on Numerical Methods and Computer Applications, 2010, 31(3): 232-240 | |
| Authors: | Wang Jiangtao Zhang Zhongzhi Xie Dongxiu Lei Xiuren |
| Affiliation: | Wang Jiangtao Zhang Zhongzhi Xie Dongxiu Lei Xiuren (Department of Mathematics, South China University of Technology, Guangzhou 510640, China; School of Business and administration, South China University of Technology, Guangzhou 510640, China)(School of Computer Science and Technology, Dongguan University of Technology, Dongguan 523808, Guangdong, China)(School of Sciences, Beijing Information Science and Technology University, Beijing 100192, China)(Department of Mathematics, South China University of Technology, Guangzhou 510640, China) |
| Abstract: | The best approximation correct a stiffness and a mass problem with the given spectral matrix in the Vibration Control constraints is usually used to Based on the denotative the- orem of Hermitian-reflexive matrices, the author discuses the inverse generalized eigenvalue problem of Hermitian-reflexive and obtain the the general expression of the solution by using the straightened matrices and the Kronecker product of matrices. Furthermore, for any given complex matrices of dimension n, the expression of solution for its optimal approximate are presented by using the Moore-Penrose generalized inverse and the best approximation theory. |
| Keywords: | Hermitian-Reflexive Matrices Generalized eigenvalue Straightened ma-trix Optimal approximation |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |