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

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.