[petsc-users] How to calculate Induced Norm of Matrix?

[Matthew Knepley]

On Sun, Oct 30, 2011 at 3:57 PM, behzad baghapour <
behzad.baghapour at gmail.com> wrote:

> So, this means there is no clear way to obtain Induced Norm of matrix like
> NORM-2 ( unless using SVD and maximum SV ) ?


I say yes. I invite you to examine the literature.

  Matt


> On Sun, Oct 30, 2011 at 7:22 PM, Matthew Knepley <knepley at gmail.com>wrote:
>
>> On Sun, Oct 30, 2011 at 3:50 PM, behzad baghapour <
>> behzad.baghapour at gmail.com> wrote:
>>
>>> OK. Thanks.
>>
>>
>> More commentary: There are lots of papers about estimating these norms
>> (1-norms too), and
>> nothing works well. There are no good ways to generically approximate the
>> matrix norm. For
>> certain very special classes of matrix, you can do it, but these are also
>> the matrices for which
>> you have a specialize very fast solver, like the Laplacian, so you rarely
>> care.
>>
>>      Matt
>>
>>
>>> On Sun, Oct 30, 2011 at 7:17 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:
>>>
>>>> On Sun, Oct 30, 2011 at 09:43, behzad baghapour <
>>>> behzad.baghapour at gmail.com> wrote:
>>>>
>>>>> Is there any way in Petsc to obtain Induced norm of matrix? (
>>>>> especially NORM-2 )
>>>>>
>>>>
>>>> Estimate the largest singular value using a Krylov method.
>>>>
>>>
>>>
>>>
>>> --
>>> ==================================
>>> Behzad Baghapour
>>> Ph.D. Candidate, Mechecanical Engineering
>>> University of Tehran, Tehran, Iran
>>> https://sites.google.com/site/behzadbaghapour
>>> Fax: 0098-21-88020741
>>> ==================================
>>>
>>>
>>
>>
>> --
>> 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
>>
>
>
>
> --
> ==================================
> Behzad Baghapour
> Ph.D. Candidate, Mechecanical Engineering
> University of Tehran, Tehran, Iran
> https://sites.google.com/site/behzadbaghapour
> Fax: 0098-21-88020741
> ==================================
>
>


-- 
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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