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

Matthew Knepley knepley at gmail.com
Tue Aug 7 08:59:05 CDT 2012

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.


>      Thanks.
>                                                        Jim
> >>在 2012-07-11 22:19:51,"Jed Brown" <jedbrown at mcs.anl.gov> 写道:
> >>On Wed, Jul 11, 2012 at 8:51 AM, w_ang_temp <w_ang_temp at 163.com> wrote:
>> >>Hello,
>> >>    Is there function in PETSc for judging the properties of the matrix
>> A ? Such as positive definitiveness and
>> >>conditional number. I know that there are several functions begin with
>> MatIs+, but it has limited amounts.
> >The Ritz values are estimates of the eigenvalues that you can obtain
> using KSPSolve() with ->ksp_compute_eigenvalues or -ksp_plot_eigenvalues.
> Note that these are estimates for the _preconditioned_ >operator, so you
> should use -pc_type none if you want estimates for the original operator.
> >http://www.mcs.anl.gov/petsc/documentation/faq.html#conditionnumber<http://www.mcs.anl.gov/petsc/documentation/faq.html#conditionnumber>

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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