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# Efficient single band eigenvalue-minimization

${\displaystyle \langle b_{i}|{\bf {H}}-\epsilon {\bf {S}}|b_{j}\rangle =0}$
${\displaystyle b_{i,i=1,N-1}=\{\phi _{n}/g_{n}^{1}/g_{n}^{2}/g_{n}^{3}/...\}.}$
The lowest eigenvector of the eigenvalue problem is used to calculate a new (possibly preconditioned) search vector ${\displaystyle g_{n}^{N}}$.