Re: [ublas] matrix exponential

Subject: Re: [ublas] matrix exponential
From: Tom Vercauteren (tom.vercauteren_at_[hidden])
Date: 2010-10-21 02:04:45

Hi,

I haven't had the chance to sufficiently test it myself to report how
good it is, but the following link provides a pure ublas way of
computing the matrix exponential:
http://www.guwi17.de/ublas/examples/

Hope this helps,
Tom

On Wed, Oct 20, 2010 at 21:14, Kraus Philipp <philipp.kraus_at_[hidden]> wrote:
>
> Am 20.10.2010 um 20:29 schrieb Thomas Klimpel:
>
>> 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.
>
> Thank for the answer. Do you know which method is faster? Do you have any
> numerical information, to do the exponential algorithm? I know Schur
> decomposition, eigen-decomposition and the algebraic definition for the
> exponential, but I must learn how to use the decomposition for the algorithm
>
> Thanks
>
> Phil
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