New Method for Eigenvector-Sensitivity Analysis with Repeated Eigenvalues and Eigenvalue Derivatives

摘要

This paper proposes a new method of eigenvector-sensitivity analysis for real symmetric systems with repeated eigenvalues and eigenvalue derivatives. The derivation is completed by using information from the second and third derivatives of the eigenproblem, and is applicable to the case of repeated eigenvalue derivatives. The extended systems with a nonsingular coefficient matrix are constructed to calculate the particular solutions. An efficient approach is developed to compute the homogeneous solutions associated with the repeated eigenvalue derivatives. Different constraints for calculating the eigenvector sensitivities are derived and discussed. Four numerical examples are presented to demonstrate the validity of the proposed method.