单参数对称广义特征值问题重特征值的灵敏度分析

Sensitivity Analysis of Multiple Eigenvalues of Symmetric Generalized Eigenvalue Problems Dependent on One Parameter

摘要: 研究了解析依赖于单参数的对称广义特征值问题重特征值的灵敏度分析，证明了重特征值及其相应特征向量的解析性，给出了特征值一阶导数的表达式，并以数值算例验证了所给结论的正确性。

Abstract: The sensitivity analysis of multiple eigenvalues of symmetric generalized eigenvalue problems is investigated. The multiple eignevalues and corresponding eigenvectors are proved to be analytical. The first order derivatives of multiple eigenvalues are given. Finally the validity of the obtained results is illustrated by a numerical example.