A new iterative method for many eigenpair partial derivatives

A new iterative method is proposed for computing partial derivatives of many eigenpairs. This method simultaneously computes a few eigenpair partial derivatives. For each origin shift, partial derivatives of eigenpairs whose eigenvalues are closest to the origin shift can be computed. Hence, this method may be used for partial derivatives of all eigenpairs. Convergence of the proposed method is established. Finally numerical experiments are given to show the effectiveness of the proposed method.