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

Barry Smith bsmith at mcs.anl.gov
Wed Jan 16 11:23:25 CST 2008


      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.


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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