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Simple Davidson iteration scheme

The preconditioned residual vector is calculated for each band resulting in a $ 2*N_{bands}$ basis-set

$\displaystyle b_{i,i=1,2*{ N_{\rm bands}}} = \{ \phi_{n} / p_{n} \vert n=1,N_{\rm bands} \}.

Within this subspace the NBANDS lowest eigenfunctions are calculated solving the eigenvalue problem

$\displaystyle \langle b_i \vert {\bf H} - \epsilon_j {\bf S} \vert b_j \rangle = 0.

The NBANDS lowest eigenfunctions are used in the next step.

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