多参数多项式特征值问题重特征值的灵敏度分析

Sensitivity Analysis of Repeated Eigenvalues of Polynomial Eigenvalue Problems Dependent on Multiparameters

研究了多参数多项式特征值问题重特征值的灵敏度,给出了多项式重特征值灵敏度的表达式.在此基础上,利用矩阵广义逆,分别给出了异导特征值和等导特征值相应特征向量一阶导数的算法,并以数值算例验证了所得结论的正确性.

The sensitivity of multiple eigenvalues of polynomial eigenvalue problems is analyzed and a sensitivity expression is derived. Based on it, the formulae for calculating the first order derivatives of the corresponding eigenvectors are given with unequal derivative eigenvalues and equal derivative eigenvalues by using generalized inverses of matrix. Finally the validity of the obtained results is illustrated by a numerical example.