矩阵方程A^TXA=C的对称M对称最佳逼近解

Symmetric M Symmetric Optimal Approximation Solution of Matrix Equation A^TXA=C

在结构动态模型修正中,通常需要修正刚度矩阵与质量矩阵以满足正交条件。通过研究它们的极小二乘逼近解对其进行修正。故在对称M对称矩阵集中,利用标准相关分解(CCD),获得了矩阵方程A^TXA=C的对称M对称极小二乘解;在此基础上应用广义奇异值分解(GSVD)和投影定理,得到了给定矩阵的极小二乘解的对称M对称最佳逼近解。

In the dynamic model updating,it usually needs to modify the stiffness matrix and the mass matrix to satisfy the orthogonal conditions. In this paper,they are modified by the study of their leastsquares approximations. Then we obtain the symmetric M symmetric least square solution ＇s of A^T XA = C by using canonical correlation decomposition in the symmetric M symmetric matrices set;Based on this,by using the projection theorem and the generalized singular value decomposition,we get its symmetric M symmetric optimal approximation solution of a given matrix.