[Trilinos-Users] GMRES faster than CG

David M Day dmday at sandia.gov
Thu Jun 19 10:06:07 MDT 2008

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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