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Subject: Re: [ublas] matrix exponential
From: Kraus Philipp (philipp.kraus_at_[hidden])
Date: 2010-10-20 15:14:02
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