A modified harmonic block Arnoldi algorithm with adaptive shifts for large interior eigenproblems

作者：Wu Gang^*

来源：Journal of Computational and Applied Mathematics, 2007, 205(1): 343-363.

DOI：10.1016/j.cam.2006.05.035

• interior eigenproblems
• block Arnoldi process
• harmonic Arnoldi method
• harmonic Ritz vectors
• modified harmonic Ritz vectors

The harmonic block Arnoldi method can be used to find interior eigenpairs of large matrices. Given a target point or shift tau to which the needed interior eigenvalues are close, the desired interior eigenpairs are the eigenvalues nearest tau and the associated eigenvectors. However, it has been shown that the harmonic Ritz vectors may converge erratically and even may fail to do so. To do a better job, a modified harmonic block Arnoldi method is coined that replaces the harmonic Ritz vectors by some modified harmonic Ritz vectors. The relationships between the modified harmonic block Arnoldi method and the original one are analyzed. Moreover, how to adaptively adjust shifts during iterations so as to improve convergence is also discussed. Numerical results on the efficiency of the new algorithm are reported.

• 出版日期2007-8-1
• 单位江苏师范大学