Iterative Computation of Eigenvector Derivatives for Middle Eigenvalues

Abstract

The computation of eigenvector derivatives for middle eigenvalues in the real symmetric eigensystems is discussed. Based on finite element modeling, the coefficient matrices of the governing equations for eigenvector derivatives are singular. This work concentrates on a new method for such computations. The method is based on an iteration technique and its convergence is proved. The number of iterations is adaptively determined based on some error estimation. Highly accurate approximations to eigenvector derivatives can be achieved with low computational cost. The proposed method can deal with both cases of simple and repeated eigenvalues in a unified manner. It is especially suitable for the large sparse matrices from finite element models. Finally, three examples including an aircraft wing structure are used to demonstrate the effectiveness of the proposed method.