Simultaneous iterative method for the derivatives of several eigenpairs of unsymmetric damped systems

In this paper, a new iterative method is proposed to calculate a few eigenpair derivatives of damped systems. The proposed method simultaneously computes the derivatives of several simple eigenvalues and their corresponding eigenvectors. Eigenpair derivatives are directly determined in n-space. Moreover, our method does not require the left eigenvectors. Convergence theory of the proposed method is given. On these grounds, using vector ϵ-algorithm, acceleration techniques for our method are provided and analyzed. Finally some numerical experiments are reported to show the efficiency of the proposed methods.