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# RMM-DIIS

${\displaystyle \langle R_{n}|R_{n}\rangle =\langle \phi _{n}|(H-\epsilon )^{+}(H-\epsilon )|\phi _{n}\rangle ,}$
and possesses a quadratic unrestricted minimum at the each eigenfunction ${\displaystyle \phi _{n}}$. If you have a good starting guess for the eigenfunction it is possible to use this algorithm without the knowledge of other wavefunctions, and therefore without the explicit orthogonalization of the preconditioned residual vector (eq. for ${\displaystyle g_{n}}$ in Single band steepest descent scheme). In this case, after a sweep over all bands a Gram-Schmidt orthogonalization is necessary to obtain a new orthogonal trial-basis set. Without the explicit orthogonalization to the current set of trial wavefunctions all other algorithms tend to converge to the lowest band, no matter from which band they started.