Jason Grout wrote: > John Cremona wrote: >> 2009/2/27 Jason Grout <jason-s...@creativetrax.com>: >>> 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. > > > I looked, and we actually use the scipy matrix exponential function. I > copied this message to the scipy dev list and CC'd you, John. > > See: http://projects.scipy.org/pipermail/scipy-dev/2009-February/011427.html > > FYI, the list is the scipy-dev list; see http://www.scipy.org/Mailing_Lists
John answered a query from the scipy-dev list and said that the following paper looked like the stuff Higham talked about: A New Scaling and Squaring Algorithm for the Matrix Exponential (with Awad Al-Mohy), MIMS EPrint 2009.9, January 2009. [new] http://eprints.ma.man.ac.uk/1217/01/covered/MIMS_ep2009_9.pdf John also provided the following link to Higham's website: "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." I'm posting these here instead of just referring to the scipy-dev thread so that we have a record of it, given that an arbitrary-precision version would probably be interesting to us. Thanks, Jason --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
