[petsc-users] minres and gmres difference

[Matthew Knepley]

On Tue, Mar 1, 2011 at 2:45 PM, Umut Tabak <u.tabak at tudelft.nl> wrote:

> Dear list,
>
> While testing an ill-conditioned system solution with minres and
> gmres(default 30 restarts, and no other options) in PETSc, I came up with
> the result that the system is solved in 155 iterations by minres to a
> relative default tolerance but it could not be solved by gmres.
>
> The original system is indefinite and had a condition number on the order
> of 10e+6, with a diagonal conditioning left and right, I could lower the
> condition number to the order of 10e+4 (however still indefinite with
> negative eigenvalues) and try to solve this system. On the other hand, I am
> also trying to understand the details of minres and gmres, so they both
> minimize the 2 norm of residual by solving a least squares problem where the
> latter is for unsymmetric systems, and the other is using a 3-term
> recurrence relation similar to cg (which I am trying to figure out now.). I
> would expect both to give the same result in PETSc however gmres fails. I
> wanted to check also gmres because I read in
>
> "Iterative Krylov Methods for Large Linear Systems" van der Vorst, Chap.6
> Gmres and Minres, page 86
>
> where it is mentioned that gmres could be more robust and less vulnerable
> to rounding errors than minres.
>

Henk did not count on different orhogonalization strategies. Try
-ksp_gmres_modifiedgramschmidt

   Matt


> What could be the reason for this? Any comments are appreciated
>
> Best,
> Umut
>



-- 
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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20110301/7d0c236a/attachment.htm>