[Pw_forum] slow relaxing

[Stefano Baroni]

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)

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de la pensée - Jean Piaget

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