A development of modal expansion method for eigensensitivity analysis of a defective matrix

摘要

In Zhang and Zhang (2006) [Z.Y. Zhang, H.S. Zhang, Calculation of eigenvalue and eigenvector derivatives of a defective matrix, Applied Mathematics and Computation 176 (2006) 7–26] a modal expansion method for eigensensitivity analysis of a defective matrix was developed, where all of the eigenvalues of the derived eigenvalue problem for the first-order eigenvalues derivatives are simple. In this paper the work is extended to the case where the derived eigenvalue problem has repeated eigenvalues. The formulas for calculating the differentiable eigenvectors, the first- to third-order eigenvalue derivatives and the first-order eigenvector derivatives are derived. A numerical example shows the validity of the method.