ON CALCULATION OF SENSITIVITY FOR NON-DEFECTIVE EIGENPROBLEMS WITH REPEATED ROOTS

Abstract

Methods of calculating eigensolution sensitivity have long been divided into two categories: the modal methods and the direct methods. This paper presents a unified theory for the calculation of derivatives of eigenvalues and eigenvectors, where the most general case, non-defective eigenproblems with repeated roots, is considered. The intrinsic relation between these two methods is exposed. The present modal method is shown to be actually the asymptotic expansion of a special direct method. A numerical example is given to verify the validity of the presented formulae, and the issue of computational efficiency is addressed.