A Shift-Deflation Technique for Computing a Large Quantity of Eigenpairs of the Generalized Eigenvalue Problems
Author:
Wei Wei,Chen Xiaoping,Shi Xueying,Luo An
Abstract
In this paper, we propose a shift-deflation technique for the generalized eigenvalue problems. This technique consists of the following two stages: the shift of converged eigenvalues to zeros, and the deflation of these shifted eigenvalues. By performing the above technique, we construct a new generalized eigenvalue problem with a lower dimension which shares the same eigenvalues with the original generalized eigenvalue problem except for the converged ones. In addition, we consider the relations of the eigenvectors before and after performing the technique. Finally, numerical experiments show the effectiveness and robustness of the proposed method.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Jiangsu Province
Natural Science Foundation of Jiangsu Higher Education Institutions of China
China Postdoctoral Science Foundation
Qing Lan Project of the Jiangsu Higher Education Institutions
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference14 articles.
1. Saad, Y. (1992). Numerical Methods for Large Eigenvalue Problems, Manchester University Press.
2. Poedts, S., Meijer, P.M., Goedbloed, J.P., van der Vorst, H., and Jakoby, A. (1994). Parallel Magnetohydrodynamics on the CM-5. High-Performance Computing and Networking, Springer.
3. Subspace iteration for eigen-solution of fluid-structure interaction problems;Yu;J. Press. Vessel Technol. ASME,1987
4. Brebbia, C.A., and Venturini, W.S. (1987). Boundary Element Techniques: Applications in Fluid Flow and Computational Aspects, Computational Mechanics Publications.
5. An algorithm for generalized matrix eigenvalue problems;Moler;SIAM J. Numer. Anal.,1973