[petsc-users] How to choose a suitable restarted m when using GMRES?

Jed Brown jedbrown at mcs.anl.gov
Sat Nov 24 09:28:51 CST 2012

On Sat, Nov 24, 2012 at 1:14 PM, w_ang_temp <w_ang_temp at 163.com> wrote:

> Hello,
>     As is know, GMRES(m) is a very efficient solver when dealing with
> symmetric indefinite
> system.

If you use an SPD preconditioner, then MINRES is equivalent to full GMRES
(without restarts), but uses a short recurrence.

> And the restarted parameter *m* is critical. When the system is small, I
> can do
> several tests to find a suitable *m*. But when the system is very large,
> it is very difficult
> to do that. I read lots of papers about GMRES(*m*) and find that almost
> none told the way to
> get a suitable *m*. Someone told me that I can just choose the matrix
> dimension as the *m*, but
> I find that it is not right.

Using that restart makes GMRES just an inefficient way to compute a dense
QR factorization, impractical unless the method converges much sooner.

In practice, you choose the restart length to balance the cost of
orthogonalizing and storage with the convergence rate.

>     So, generally, when using GMRES(*m*) as the sovler, how to use a
> suitable restarted *m*?
>     Thanks.
>                                                                Jim
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