A block Chebyshev-Davidson method with inner-outer restart for large eigenvalue problems

作者：Zhou Yunkai^*

来源：Journal of Computational Physics, 2010, 229(24): 9188-9200.

DOI：10.1016/j.jcp.2010.08.032

• Chebyshev polynomial filter
• Chebyshev-Davidson method
• Subspace iteration
• Restart
• Block method
• Block-wise filtering
• Eigenproblem

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.

• 出版日期2010-12-10