Fast inexact subspace iteration for generalized eigenvalue problems with spectral transformation |
| |
Authors: | Fei Xue |
| |
Institution: | a Applied Mathematics and Scientific Computation Program, Department of Mathematics, University of Maryland, College Park, MD 20742, USA b Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, USA |
| |
Abstract: | We study inexact subspace iteration for solving generalized non-Hermitian eigenvalue problems with spectral transformation, with focus on a few strategies that help accelerate preconditioned iterative solution of the linear systems of equations arising in this context. We provide new insights into a special type of preconditioner with “tuning” that has been studied for this algorithm applied to standard eigenvalue problems. Specifically, we propose an alternative way to use the tuned preconditioner to achieve similar performance for generalized problems, and we show that these performance improvements can also be obtained by solving an inexpensive least squares problem. In addition, we show that the cost of iterative solution of the linear systems can be further reduced by using deflation of converged Schur vectors, special starting vectors constructed from previously solved linear systems, and iterative linear solvers with subspace recycling. The effectiveness of these techniques is demonstrated by numerical experiments. |
| |
Keywords: | Inexact subspace iteration Tuned preconditioner Deflation Subspace recycling Starting vector |
本文献已被 ScienceDirect 等数据库收录! |
|