Conjugate gradient optimization
Instead of the previous iteration scheme, which is just some kind of Quasi-Newton scheme, it also possible to optimize the expectation value of the Hamiltonian using a successive number of conjugate gradient steps. The first step is equal to the steepest descent step in section \ref{min-en2}. In all following steps the preconditioned gradient [math]\displaystyle{ g^N_{n} }[/math] is conjugated to the previous search direction. The resulting conjugate gradient algorithm is almost as efficient as the algorithm given in Single band steepest descent scheme. For further reading see [1][2][3].