On calculation of sensitivity for non-defective eigenproblems with repeated roots

Methods of calculating eigensolution sensitivity have long been divided int o two categories: the modal methods and the direct methods. This paper pres ents a unified theory for the calculation of derivatives of eigenvalues and eigenvectors, where the most general case, non-defective eigenproblems wit h repeated roots, is considered. The intrinsic relation between these two m ethods is exposed. The present modal method is shown to be actually the asy mptotic expansion of a special direct method. A numerical example is given to verify the validity of the presented formulae, and the issue of computat ional efficiency is addressed. (C) 1999 Academic Press.