Calculation of eigenpair derivatives for symmetric quadratic eigenvalue problem with repeated eigenvalues

Abstract

In this paper, we consider computing the derivatives of the semisimple eigenvalues and corresponding eigenvectors of symmetric quadratic eigenvalue problem. In the proposed method, the eigenvector derivatives of the symmetric quadratic eigenvalue problem are divided into a particular solution and a homogeneous solution; a simplified method is given to calculate the particular solution by solving a linear system with nonsingular coefficient matrix, the method is numerically stable and efficient. Two numerical examples are included to illustrate the validity of the proposed method.