[Trilinos-Users] GMRES faster than CG

[Heroux, Michael A]

Rony,

AztecOO uses right preconditioning.  The attraction of  this approach is that the (usually approximate) residual values generated by the iterative process correspond to the unpreconditioned residual and are generally easier to use as a diagnostic for convergence.

Mike


On 6/25/08 4:43 AM, "Rony Speck" <speckro at hotmail.com> wrote:



Thanks a lot for the answer, Mr. Day.

I have another question. How is the preconditioning done inside AztecOO? Is it always a left-preconditioning for both GMRES and CG?
Or does it depend on the preconditioner used?

Thanks in advance

----------------------------------------
> Subject: Re: [Trilinos-Users] GMRES faster than CG
> From: dmday at sandia.gov
> To: speckro at hotmail.com; trilinos-users at software.sandia.gov
> Date: Thu, 19 Jun 2008 10:06:07 -0600
>
> Dear Rony Speck,
> I am a Mathematican, not a Computer Scientist, but the mathematical
> differences between CG and GMRES help to explain your observations.  The
> MRES in GMRES refers to minimizing the norm of the residual at
> each iteration.  CG on the other hand minimizes a norm of the solution
> error.  This is why residual error norms for GMRES decrease
> monotonically, but not for CG.  Both algorithms work essentially the
> same with preconditioners.  However the preconditioner changes the
> subspace generated, and the norms used.  --David Day
>
>
>
>
>
>
>
>
>
>
> On Thu, 2008-06-19 at 03:50 -0600, Rony Speck wrote:
>> Hello everybody
>>
>> When using AztecOO, I noticed that GMRES converges faster and needs less time than CG when using IFPACK IC or ML as a preconditioner.
>> The difference is quite large. The system is spd. When using no preconditioner, CG needs less iterations and is faster.
>> I also plotted the iteration numbers against the norms of the residuals. For GMRES the curve is smooth, whereas for
>> CG the curve is rather erratic. For both solvers I set the convergence criterium to AZ_rhs.
>>
>> Has anyone else experienced this?
>>
>> Thanks for your answers
>> Rony Speck
>>
>>
>> _________________________________________________________________
>> Sie haben nie Platz in Ihrer Inbox? Mit Windows Live Hotmail haben Sie jetzt 5GB Speicherplatz - gratis! Holen Sie sich hier Ihren neuen  Windows Live Hotmail Account!
>> http://get.live.com/mail/overview
>>
>> _______________________________________________
>> Trilinos-Users mailing list
>> Trilinos-Users at software.sandia.gov
>> http://software.sandia.gov/mailman/listinfo/trilinos-users
>
>

_________________________________________________________________
Sie haben nie Platz in Ihrer Inbox? Mit Windows Live Hotmail haben Sie jetzt 5GB Speicherplatz - gratis! Holen Sie sich hier Ihren neuen  Windows Live Hotmail Account!
http://get.live.com/mail/overview

_______________________________________________
Trilinos-Users mailing list
Trilinos-Users at software.sandia.gov
http://software.sandia.gov/mailman/listinfo/trilinos-users


-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://software.sandia.gov/mailman/private/trilinos-users/attachments/20080625/e2cfb89e/attachment-0001.html