[SciPy-dev] Matrix exponential
jason-sage@creativetra...
jason-sage@creativetra...
Sat Feb 28 04:09:50 CST 2009
(It appears that this postscript from John (at the top of the message
below) didn't make it to the scipy-dev list, probably because he's not
subscribed, so I'm forwarding the message to the scipy-dev list.)
-Jason
John Cremona wrote:
> PS An interesting quote from one of Higham's talks:
>
> The availability of expm(A) in
> early versions of MATLAB
> quite possibly contributed to
> the system’s technical and commercial success.”
> — Cleve Moler (2003)
>
> I get the impression that this is used a lot, though they only seem to
> want double precision (as opposed to multi) which is both fast and has
> predictably bounded error. The method is a variant of a standard one
> (Pade approximations) with some nice tricks as some once-and-for all
> parameter tuning (for which he said they used Maple!)
>
> John Cremona
>
> 2009/2/27 <jason-sage@creativetrax.com>:
>
>> 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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