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A block Chebyshev-Davidson method with inner-outer restart for large eigenvalue problems
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DOI：10.1016/j.jcp.2010.08.032.png)
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Abstract
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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. (C) 2010 Elsevier Inc. All rights reserved.
Keywords:
Chebyshev polynomial filter
Chebyshev-Davidson method
Subspace iteration
Restart
Block method
Block-wise filtering
Eigenproblem
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