whether do I need to consider the symmetric preconditioner when using CG?

[Yujie]

Dear Barry:

Thank you for your explanation. Currently, I am reading Yousef Saad's book,
Iterative methods for sparse linear systems. Therefore, I have such a
problem. Thanks again.

Regards,
Yujie

On 1/16/08, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>
>    Yujie,
>      I now understand the reason for your question. CG can be implemented
> with right, left or split preconditioner and in
> ALL three cases it is still a symmetric implementation of CG! All give
> similar convergence rates.
>
>     The largest effect of left, right or split is in stopping criteria;
> right preconditioning always uses the TRUE residual
> norm to determine convergence || b - A x||, left preconditioning using ||
> B(b - Ax) ||. You can use
> -ksp_norm_type unpreconditioned  with left preconditioner or natural norm.
> You can see the code KSPSolve_CG
> for exact details.
>
>    Barry
>
>
> On Jan 16, 2008, at 11:15 AM, Yujie wrote:
>
> Dear Lisandro:
>
> From PETSc manual, I know KSPCG only supports left preconditioning.
> However, I want to know whether does this affect the performance of
> preconditioned CG? The main problem is that it should be better to generate
> a symmetric preconditioned operator for CG method. However, Left
> preconditioner should have some difficulty to get such operator? Do you have
> any testings about it regarding left, split and right preconditinoers and CG
> realization in PETSc? thanks a lot.
>
> Regards,
> Yujie
>
> On 1/16/08, Lisandro Dalcin <dalcinl at gmail.com> wrote:
> >
> > KSPCG only supports left preconditioning.
> >
> > On 1/16/08, Yujie <recrusader at gmail.com> wrote:
> > > hi, everyone
> > >
> > > I know there are three types of preconditioners, that is left, split
> > and
> > > right preconditioners? When I use CG method in PETSc, whether do I
> > need to
> > > consider select one type of preconditioner? Whether do different types
> > > affect the performance of preconditioned CG? thanks a lot.
> > >
> > > Regards,
> > > Yujie
> > >
> >
> >
> > --
> > Lisandro Dalcín
> > ---------------
> > Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC)
> > Instituto de Desarrollo Tecnológico para la Industria Química (INTEC)
> > Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
> > PTLC - Güemes 3450, (3000) Santa Fe, Argentina
> > Tel/Fax: +54-(0)342-451.1594
> >
> >
>
>
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