a few remarks for the benefit of the less experienced members of the forum:
On May 11, 2008, at 10:22 AM, Nicola Marzari wrote: > ideally, if you have 18 atoms, i.e. 56 degrees of freedom (or 53, if > you > remove traslations) a conjugate gradient algorithms should bring you > to > the minimum in 53 steps. this is strictly true for a quadratic function. a non quadratic one may require more iterations. also, the number of degrees of freedon should be considered as an upper bound for the number of iterations needed to minimize a quadratic functional using CG's. this upper limit is only reached for very ill-conditioned functionals (those whose quadratic form has eigenvalues of wildly different order of magnitude). well conditioned functionals (whose quadratic form has eigenvalues all of about the same magnitude) usually converge much faster. to some extent, the above two facts (non quadraticity, better condition of the quadratic form) and may compensate, I guess. Stefano --- Stefano Baroni - SISSA & DEMOCRITOS National Simulation Center - Trieste [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype) La morale est une logique de l'action comme la logique est une morale de la pens?e - Jean Piaget Please, if possible, don't send me MS Word or PowerPoint attachments Why? See: http://www.gnu.org/philosophy/no-word-attachments.html -------------- next part -------------- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20080511/dbd10dca/attachment.htm
