论文信息 - A new restarting method in the harmonic projection algorithm for computing the eigenvalues of a nonsymmetric matrix

A new restarting method in the harmonic projection algorithm for computing the eigenvalues of a nonsymmetric matrix

The harmonic projection method can be used to find interior eigenpairs of large matrices. Given a target point or shift τ to which the needed interior eigenvalues are close, the desired interior eigenpairs are the eigenvalues nearest τ and the associated eigenvectors. However, it has been shown that the harmonic projection method may converge erratically and even may fail to do so. In this paper, we present a new restarting method in the harmonic projection algorithm for computing the eigenvalues of a nonsymmetric matrix. The implementation of the algorithm has been tested by numerical examples, the results show that the algorithm converges fast and works with high accuracy.

H. Saberi Najafi | Hossein Moosaei

[1] H. Saberi Najafi,et al. A new restarting method in the Arnoldi algorithm for computing the eigenvalues of a nonsymmetric matrix , 2004, Appl. Math. Comput..

[2] H. Saberi Najafi,et al. Weighted restarting method in the weighted Arnoldi algorithm for computing the eigenvalues of a nonsymmetric matrix , 2006, Appl. Math. Comput..

[3] R. Morgan,et al. Harmonic projection methods for large non-symmetric eigenvalue problems , 1998 .

[4] Gang Wu. A modified harmonic block Arnoldi algorithm with adaptive shifts for large interior eigenproblems , 2007 .

[5] Min Zeng,et al. Harmonic projection methods for large non-symmetric eigenvalue problems , 1998, Numer. Linear Algebra Appl..

[6] H. Saberi Najafi,et al. A new restarting method in the Lanczos algorithm for generalized eigenvalue problem , 2007, Appl. Math. Comput..