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.
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.
出处
《数值计算与计算机应用》
CSCD
北大核心
2010年第3期232-240,共9页
Journal on Numerical Methods and Computer Applications
基金
国家自然科学基金(10971058)
北京市教学名师建设项目(61N0810810)
关键词
埃尔米特自反矩阵
广义特征值
矩阵拉直
最佳逼近
Hermitian-Reflexive Matrices
Generalized eigenvalue
Straightened ma-trix
Optimal approximation
