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

w_ang_temp w_ang_temp at 163.com
Sat Nov 24 10:38:09 CST 2012

>>On 2012-11-24 23:28:51,"Jed Brown" <jedbrown at mcs.anl.gov> 写道:
>>On Sat, Nov 24, 2012 at 1:14 PM, w_ang_temp <w_ang_temp at 163.com> wrote:

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

>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, is there no effective way to determine a suitable m? Only by doing lots of tests to find
an appropriate value in practical application? Or something need to be noticeable of using GMRES
with an effective way?
>>    So, generally, when using GMRES(m) as the sovler, how to use a suitable restarted m?
>>    Thanks.
>>                                                               Jim

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