[Trilinos-Users] GMRES faster than CG

Rony Speck speckro at hotmail.com
Wed Jun 25 03:43:55 MDT 2008


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
>> 
>> 
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