The preconditioned residual vector is calculated for each band resulting in
Within this subspace the NBANDS lowest eigenfunctions are calculated
solving the eigenvalue problem
The NBANDS lowest eigenfunctions are used in the next step.
Implemented Davidson-block iteration scheme
The implemented scheme selects a subset of all bands from . The following steps are then performed on this subset:
- Optimize this subset by adding the orthogonalized preconditioned residual vectors to the presently
- Apply Rayleigh-Ritz optimization in the space spanned by these vectors (``sub-space rotation in a dim. space) to determine the lowest vectors .
- Add additional preconditioned residuals calculated from the yet optimized bands
- Sub-space rotation in a dim. space.
- Continue iteration by adding a fourth set of preconditioned vectors if required. If the iteration is finished, store the optimized wavefunction back in the set
- Continue with next sub-block .
- After each band has been optimized a Raighly Ritz optimization in the space
This method is approximately a factor of 1.5-2 slower than RMM-DIIS, but always stable. It is available in parallel for any data distribution.