Conjugate Gradient technique

[Barai, Pallab]

Hello Matt,

Thank you very much for your reply. 

Here "S" is a symmetric matrix, so I have to use the CG.

But I can not figure out how to use the Conjugate Gradient technique to find the solution. In the "MatShell" I can wrap my "MatVec" routine which calculates the "S*x" vector. 

But how will I be able to do the comparison between the known "b" vector and the calculated "S*x" using a CG (and come up with a new trial solution "x" for the next iteration). What is the function that I should call for this purpose?

Thanking you.

Pallab


-----Original Message-----
From: petsc-users-bounces at mcs.anl.gov on behalf of Matthew Knepley
Sent: Thu 5/14/2009 5:03 PM
To: PETSc users list
Subject: Re: Conjugate Gradient technique
 
On Thu, May 14, 2009 at 3:58 PM, Barai, Pallab <baraip at ornl.gov> wrote:

> Hello,
>
> I am using PETSc to solve a set of linear equations "Sx=b".
>
> Here "b" is known and "x" is the trial solution.
>
> The complete (assembled) form of S is not known. That is why I am not able
> to use something like "KSPSolve".
>
> But given a trial solution "x", I can calculate "S*x" using a "MatVec"
> routine.
>
> Is it possible to use the Conjugate Gradient (CG) technique to find a
> solution in this case? In place of "S", I can give "S*x" as the input.


You can use CG if S is symmetric. If not, try GMRES.


>
> It will be great if someone can show me some direction. If this thing has
> already been discussed before, the link to that thread will be sufficient.


You can wrap your function in a MatShell:

http://www.mcs.anl.gov/petsc/petsc-as/snapshots/petsc-current/docs/manualpages/Mat/MatCreateShell.html

   Matt


>
> Thanking you.
>
> Pallab Barai
>
-- 
What most experimenters take for granted before they begin their experiments
is infinitely more interesting than any results to which their experiments
lead.
-- Norbert Wiener