how to get all the singular values of the matrix?

[Hong Zhang]

Yujie,
>
> Based what you said, it looks like a little difficult to evalute the matrix
> in PETSc, especailly regarding a big dimension. However, when I select
> iterative methods, how to select a suitable one based on some evaluation?
> Could you give me some advice? thanks a lot.

What do you mean "how to select a suitable one based on some evaluation?"
Usually, one wants a few eigenvalues with largest or smallest magnitude, 
or eigenvalues in a real interval when matrix is Hermitian.
Please refer slepc user manual, which gives detailed description.

Hong
>
> Regards,
> Yujie
>
> On 1/14/08, Hong Zhang <hzhang at mcs.anl.gov> wrote:
>>
>>
>> If you want few selected eigen solutions of sparse matrix,
>> you should use sparse eigen solver. Take a look at'
>> slepc (http://www.grycap.upv.es/slepc/)
>> or use slepc interface with arpack.
>>
>> Hong
>>
>>
>> On Mon, 14 Jan 2008, Yujie wrote:
>>
>>> Thank you for your advice.
>>> I have used -ksp_compute_eigenvalues_explicitly to get the eigen values.
>>> However, it is very very
>>> slow because the dimension of the matrix is about ten thousand.
>>>
>>> Yujie
>>>
>>> On 1/14/08, Matthew Knepley <knepley at gmail.com> wrote:
>>>>
>>>> You can use
>>>>
>>>>
>>>>
>> http://www-unix.mcs.anl.gov/petsc/petsc-as/snapshots/petsc-current/docs/manualpages/KSP/KSPComputeEigenvaluesExplicitly.html
>>>>
>>>> with and without a preconditioner. We have not coded the SVD
>>>> counterpart, but you can use
>>>>
>>>>
>>>>
>> http://www-unix.mcs.anl.gov/petsc/petsc-as/snapshots/petsc-current/docs/manualpages/KSP/KSPComputeExplicitOperator.html
>>>>
>>>> and then call the LAPACK yourself.
>>>>
>>>>   Matt
>>>>
>>>> On Jan 13, 2008 11:23 PM, Yujie <recrusader at gmail.com> wrote:
>>>>> Hi, everyone
>>>>>
>>>>> I want to select iterative methods by observing the singular values
>>>>> decompostion of the matrix. However, I don't know how to get all the
>>>>> singular values of the matrix in PETSc. I know the command
>>>>> "-ksp_monitor_singular_value" may get the max and min singular values
>> at
>>>>> each iteration. How to get the singular values of the matrix I want to
>>>>> solve? In addition, when I use the preconditioned iterative method,
>> how
>>>> to
>>>>> get the singular values of the preconditioned iterative operator?
>>>>>
>>>>> thanks a lot.
>>>>>
>>>>> Regards,
>>>>> Yujie
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> 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
>>>>
>>>>
>>>
>>
>>
>