[petsc-users] Functions for judging the properties of the matrix

[Matthew Knepley]

On Tue, Aug 7, 2012 at 9:55 AM, w_ang_temp <w_ang_temp at 163.com> wrote:

> Hello,
>     I am sorry that I cannot understand "Make sure to avoid restarts". In
> the FAQ, it says that using the restarted
> GMRES method to get approximations to the condition number. So why saying
> "avoid restarts" in the next following?
>

Jim, in order to understand this, it is necessary to understand GMRES.
Please read the section in Yousef Saad's book. We
are factoring the Hessenberg matrix it produces to get estimates. If you
restart, that is thrown away.

   Matt


>     Besides, there are two questions about GMRES:
>     (1) Is the "iterations count" of GMRES with restarted parameters which
> is outputted by PETSc meaningless?
>     (2) Is there only restarted GMRES in PETSc?
>     Thanks.
>                                                 Jim
>
>
> >>在 2012-08-07 21:59:05，"Matthew Knepley" <knepley at gmail.com> 写道：
>
> >>On Tue, Aug 7, 2012 at 8:56 AM, w_ang_temp <w_ang_temp at 163.com> wrote:
>
>>
>> >>Hello, Jed
>> >>    I am a little puzzled about the "How can I determine the condition
>> number of a matrix?" in the
>> >>FAQ. The details are as follows:
>>
>> >>    "...For larger matrices, you can run with *-pc_type none -ksp_type
>> gmres -ksp_monitor_singular_value *
>> >>*-ksp_gmres_restart 1000* to get approximations to the condition
>> number of the operator. This will
>> >>generally be accurate for the largest singular values, but may
>> overestimate the smallest singular
>> >>value unless the method has converged. Make sure to avoid restarts...".
>>
>> >>    Since the command "*-pc_type none -ksp_type gmres
>> -ksp_monitor_singular_value*
>> >>*-ksp_gmres_restart 1000*" using restart parameter, so, what does
>> "Make sure to avoid restarts" mean?
>>
>
> >Do not believe the answer after the restart.
>
>
>>  >>Besides, is the parameter "*1000*" a reference value which will be
>> changed in specific project in order
>> >>to be converged? Or must use *1000 *to get the condition number?
>>
>
> >The former.
>
>   >  Matt
>
>
>>     >> Thanks.
>>  >>                                                      Jim
>>
>
>
>


-- 
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
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