[SciPy-dev] Matrix exponential

jason-sage@creativetra... jason-sage@creativetra...
Fri Feb 27 15:52:04 CST 2009

John Cremona posted the following message to the sage development list 
about matrix exponentials.  I'm copying it to here since it asks about 
the scipy matrix exponential method (we say numpy below, but we really 
mean scipy...)

John Cremona wrote:

> >> I have just been to a colloquium talk by numerical analyst Nick Higham
> >> (Manchester) called "How to compute and not to compute a matrix
> >> exponential".  He has new methods which are now in mathematica, matlab
> >> and NAG but (apparantly) nowhere else.  He only seemed interested in
> >> getting good speed & precision to 16 decimals but (when I asked)
> >> confirmed that the methods should apply to give arbitrary precision.
> >>
> >> I just checked and see that Sage's  matrix exp() uses something stupid
> >> except over RDF/CDF where it uses a pade approximation method via
> >> numpy.  The method of the talk was a variant of that, the main trick
> >> being to use exactly the right order of Pade approx. so maximise
> >> precision and speed.
> >>
> >> I would like to know how good the numpy method is, and  whether it can
> >> be improved to this "state of the art" version at least for RDF.  Then
> >> it could be another selling point for Sage.
> Could you CC the numpy devlist as well on this?  It sounds exciting!

I will if you give me the address (or you can perhaps?).  It might be
worth including Higham's URL:
http://www.maths.manchester.ac.uk/~higham/  as he has lots of his
talks up there including some which are similar to the one I heard.

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