Re: [ublas] matrix exponential

Subject: Re: [ublas] matrix exponential
From: Kraus Philipp (philipp.kraus_at_[hidden])
Date: 2010-10-21 05:32:43

Am 21.10.2010 um 09:31 schrieb sguazt:

> On Thu, Oct 21, 2010 at 8:52 AM, David Bellot  
> <david.bellot_at_[hidden]> wrote:

> Actually, MATLAB uses Padé approximation + scaling&squaring method
> (http://www.mathworks.com/help/techdoc/ref/expm.html)
>
> Also OCTAVE seems to use the same algorithm:
> http://hg.savannah.gnu.org/hgweb/octave/file/304b0ed4ca56/scripts/linear-algebra/expm.m
>

It seems the Pad approximation is the fastest one, so I would like to  
use them

Phil

>> David
>>
>> On Wed, Oct 20, 2010 at 20:29, Thomas Klimpel <Thomas.Klimpel_at_[hidden] 
>> >
>> wrote:
>>>
>>> Kraus Philipp wrote:
>>>> I would like to create a matrix exponential
>>>> (http://en.wikipedia.org/wiki/Matrix_exponential
>>>> ) with a boost matrix. Is there any functionality within the  
>>>> boost or
>>>> the numerical bindings on LAPACK?
>>>
>>> You could use LAPACK to compute the Schur decomposition, and  
>>> compute the
>>> exponential with the help of the Schur decomposition.
>>> Or you could use LAPACK to compute the eigen-decomposition, and  
>>> compute
>>> the exponential with the help of the eigen-decomposition.
>>>
>>> The approach with the eigen-decomposition is easier to implement,  
>>> but the
>>> approach with the Schur decomposition is numerically more robust  
>>> for general
>>> matrices. But let's be honest, most of us will start with the
>>> eigen-decomposition, and the result is normally good enough so  
>>> that the
>>> approach with the Schur decomposition never actually gets  
>>> implemented.
>>>
>>> The two famous papers on this subject propose many more methods and
>>> explain their tradeoffs.
>>>
>>> Regards,
>>> Thomas
>>> _______________________________________________
>>> ublas mailing list
>>> ublas_at_[hidden]
>>> http://lists.boost.org/mailman/listinfo.cgi/ublas
>>> Sent to: david.bellot_at_[hidden]
>>
>>
>>
>> --
>> David Bellot, PhD
>> david.bellot_at_[hidden]
>> http://david.bellot.free.fr
>>
>>
>> _______________________________________________
>> ublas mailing list
>> ublas_at_[hidden]
>> http://lists.boost.org/mailman/listinfo.cgi/ublas
>> Sent to: marco.guazzone_at_[hidden]
>>
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