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

[behzad baghapour]

OK. Thanks again.

On Sun, Oct 30, 2011 at 8:10 PM, Jack Poulson <jack.poulson at gmail.com>wrote:

> Not a problem; though for some reason I repeatedly wrote "condition
> number" when I meant "two norm". Dixon's paper certainly provides a method
> for computing an estimate to the condition number, but the latter also
> requires the ability to apply the inverse of your operator and the inverse
> of its adjoint.
>
> Jack
>
>
> On Sun, Oct 30, 2011 at 11:33 AM, behzad baghapour <
> behzad.baghapour at gmail.com> wrote:
>
>> A good paper, I will work on it.
>> Thanks a lot dear Jack.
>>
>>
>> On Sun, Oct 30, 2011 at 7:54 PM, Jack Poulson <jack.poulson at gmail.com>wrote:
>>
>>> On Sun, Oct 30, 2011 at 10:52 AM, Matthew Knepley <knepley at gmail.com>wrote:
>>>
>>>> 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.
>>>>
>>>>
>>>
>>> There is a nice paper by John D. Dixon, "Estimating Extremal Eigenvalues
>>> and Condition Numbers of Matrices", http://www.jstor.org/pss/2157241,
>>> which provides an extremely robust method for getting rough estimates of
>>> the condition number, and it only requires the ability to apply your
>>> operator and its adjoint. A typical usage would be to compute an estimate
>>> of the condition number K, such that the true condition number is within a
>>> factor of 2 of K with a probability of 1-10^-6.
>>>
>>> The 1-norm is actually pretty trivial to compute if you have access to
>>> your matrix entries; it is the maximum vector one norm of the columns of
>>> the matrix.
>>>
>>> Jack
>>>
>>
>>
>>
>> --
>> ==================================
>> Behzad Baghapour
>> Ph.D. Candidate, Mechecanical Engineering
>> University of Tehran, Tehran, Iran
>> https://sites.google.com/site/behzadbaghapour
>> Fax: 0098-21-88020741
>> ==================================
>>
>>
>


-- 
==================================
Behzad Baghapour
Ph.D. Candidate, Mechecanical Engineering
University of Tehran, Tehran, Iran
https://sites.google.com/site/behzadbaghapour
Fax: 0098-21-88020741
==================================
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