N重亏损状态矩阵广义特征向量灵敏度分析

Sensitivity Analysis for Generalized Eigenvectors of N-multiple Defective State Matrice

为了克服具有N重特征值的状态矩阵发生亏损现象后对灵敏度分析的制约,本文基于亏损矩阵的若当标准形理论,引入广义特征向量及其伴随向量系,提出了广义特征向量灵敏度的全模态算法。求解亏损矩阵广义特征向量的灵敏度时,发现除一个灵敏度系数为非精确解外,其余灵敏度系数均为精确解。针对非精确解,通过引入松驰因子获得了较好的近似解。数值算例证实该算法适用于N重亏损状态矩阵的灵敏度分析。

The generalized modes method for the generalized eigenvector sensitivity analysis is presented based on the Jordan canonical form of the defective matrices in order to eliminate the influence of defective phenomenon of the corre-sponding state-matrice with N multiple eigenvalues. While the sensitivity of the generalized eigenvector of the defective matrice was solved, the results show that one of the coefficients for the sensitivity is no accurate solution, and that others are accurate. A good approximate solution can be further obtained by introducing a relaxation factors for no accu-rate solution. The numerical calculation verify that this method is suitable for the analysis of the N multiple eigenvalue’s sate-matrice.