next up previous contents
Next: 9.1.6 Residual minimization scheme Up: 9.1 Algorithms used in Previous: 9.1.4 Efficient single band

9.1.5 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 9.1.3. In all following steps the preconditioned gradient tex2html_wrap_inline4879 is conjugated to the previous search direction. The resulting conjugate gradient algorithm is almost as efficient as the algorithm given in section 9.1.4. For further reading see [18, 19, 26].

Mon Mar 29 10:38:29 MEST 1999