A parallel way for computing eigenvector sensitivity of asymmetric damped systems with distinct and repeated eigenvalues

Abstract

A high efficient method is proposed for computing the eigensolution derivatives of asymmetric damped systems with distinct and repeated eigenvalues. A new normalization for the left eigenvectors is proposed, from which a new form of the constraints of the left eigenvector sensitivities can be derived. The aim of this paper is to show how to compute the left and right eigenvector derivatives separately and independently such that those can be computed in a parallel way. In addition, the calculation of eigenvalue sensitivity of N damped asymmetric systems with repeated eigenvalues is derived. The proposed method is well-conditioned since the components of coefficient matrices are all of the same order of magnitude. The method is simple, compact and easy to be implemented on computers. Three numerical examples are used to illustrate the application, accuracy and efficiency of the proposed method.