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Conjugate gradient optimization

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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 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 [1][2][3].

References

  1. M.P. Teter, M.C. Payne and D.C. Allan, Phys. Rev. B 40, 12255 (1989).
  2. D.M. Bylander, L. Kleinman and S. Lee, Phys Rev. B 42, 1394 (1990).
  3. [ W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, em Numerical Recipes (Cambridge University Press, New York, 1986).]