Eigenvector Derivatives of Generalized Nondefective Eigenproblems With Repeated Eigenvalues

Abstract

A new method is presented for computation of eigenvalue and eigenvector derivatives associated with repeated eigenvalues of the generalized nondefective eigenproblem. This approach is an extension of recent work by Daily and by Juang et al. and is applicable to symmetric or nonsymmetric systems. The extended phases read as follows. The differentiable eigenvectors and their derivatives associated with repeated eigenvalues are determined for a generalized eigenproblem, requiring the knowledge of only those eigenvectors to be differentiated. Moreover, formulations for computing eigenvector derivatives have been presented covering the case where multigroups of repeated first eigenvalue derivatives occur. Numerical examples are given to demonstrate the effectiveness of the proposed method.