1. A block Chebyshev–Davidson method with inner–outer restart for large eigenvalue problems
- Author
-
Zhou, Yunkai
- Subjects
- *
CHEBYSHEV polynomials , *BOUNDARY value problems , *ITERATIVE methods (Mathematics) , *DENSITY functionals , *HAMILTONIAN systems , *ROBUST control , *NUMERICAL analysis - Abstract
Abstract: We propose a block Davidson-type subspace iteration using Chebyshev polynomial filters for large symmetric/hermitian eigenvalue problem. The method consists of three essential components. The first is an adaptive procedure for constructing efficient block Chebyshev polynomial filters; the second is an inner–outer restart technique inside a Chebyshev–Davidson iteration that reduces the computational costs related to using a large dimension subspace; and the third is a progressive filtering technique, which can fully employ a large number of good initial vectors if they are available, without using a large block size. Numerical experiments on several Hamiltonian matrices from density functional theory calculations show the efficiency and robustness of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF