对称广义中心对称半正定矩阵模型修正的矩阵逼近法及其应用

Matrix Approximation Method and Its Application on Generalized Symmetric Positive Semi-definite Symmetric Matrix Model Correction

设X,B分别是实测的位移矩阵和载荷矩阵,C是有限元模型估计,找对称广义中心对称半正定矩阵使‖C-‖F=min‖C-A‖_F·我们证明这样的存在唯一,并应用它来修正动力模型.数值结果证明方法是行之有效的.

Let X, B be a displacement matrix and load matrix respectively by test data. C stands for an estimate matrix of finite model. In this paper we find the matrix .4 to minimize the Frobenius norm of C - A for all symmetric generalized centro-symmetric positive semidefinite matrices A satisfying AX --- B. We prove the existence and uniqueness for such a A and apply it to update a dynamic system. Numerical results show that the method is feasible and effective.