Re: Pade Approximation (further generalizations?---feature request)

*To*: mathgroup at smc.vnet.net*Subject*: [mg109473] Re: Pade Approximation (further generalizations?---feature request)*From*: telefunkenvf14 <rgorka at gmail.com>*Date*: Wed, 28 Apr 2010 06:59:55 -0400 (EDT)*References*: <hq414o$3cd$1@smc.vnet.net> <hq61q7$3i8$1@smc.vnet.net>

On Apr 18, 4:58 am, David Reiss <dbre... at gmail.com> wrote: > On Apr 17, 6:05 am, David Reiss <dbre... at gmail.com> wrote: > > > > > On Apr 16, 5:49 am, telefunkenvf14 <rgo... at gmail.com> wrote: > > > > On Apr 14, 10:39 pm, David Reiss <dbre... at gmail.com> wrote: > > > > > Another addition to thePadeApproximant function that would be very > > > > useful would be the generalizedPadeApproximant: these arePade > > > > Approximants that are based on more than one expansion point. I cod= ed > > > > this up many years ago for some work in Radar propagation analysis > > > > (never published but I really should have...): > > > > >http://scientificarts.com/radar/radar/PadeMethod/index.html > > > > > more stuff on Radar is here... which I really should do somethin= g > > > > commercial with sometime.... > > > > >http://scientificarts.com/radar/radar/index.html > > > > > --Davidhttp://scientificarts.com/worklife > > > > > On Apr 14, 5:16 am, telefunkenvf14 <rgo... at gmail.com> wrote: > > > > > > I've been playing around with PadeApproximant[] in Mathematica an= d = > have > > > been really impressed at the accuracy of the approach. > > > > > > According to Wikipedia: > > > > > > A Pad=E9 approximant approximates a function in one variable. A= n > > > > > approximant in two variables is called a Chisholm approximant, in > > > > > multiple variables a Canterbury approximant (after Graves-Morris = at > > > > > the University of Kent). > > > > > > Does anyone know if v8 will include Chisholm and Canterbury > > > > > approximation? > > > > > > -RG > > > > Good timing! I actually came across a economics paper last night that > > > usedPadeat more than one point, so it would be nice to see how this > > > could be coded in Mathematica. > > > > Could you show me? (I understand if you don't want to, or if there ar= e > > > too many other dependencies on other package functions.) > > > > -RG > > > Let me see if I can track it down and if it is actually usable out of > > its original context ... it may not be pretty! I've learned a lot= i= > n > > the last 10 years! A good place to read up on it though is in Bender > > and Orszag if my memory serves me right: > > >http://www.amazon.com/Advanced-Mathematical-Methods-Scientists-Engine... > > > --David > > Alas, it was a rather rambling notebook with a special case > computation for the expansion of the solution of a particular > differential equation around several points. So the code is not > usable by anyone else -- and perhaps not me either anymore! > Notebook archeology.... For future reference, here is a demonstration project on Pade Approximation at multiple points: http://demonstrations.wolfram.com/MultipointPadeApproximants/ -RG