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 Single band steepest descent scheme. In all following steps the preconditioned gradient $g_{n}^{N}$ is conjugated to the previous search direction. The resulting conjugate gradient algorithm is almost as efficient as the algorithm given in Efficient single band eigenvalue-minimization. For further reading see .

---