Re: Pade Approximation (further generalizations?---feature request)
- To: mathgroup at smc.vnet.net
- Subject: [mg109223] Re: Pade Approximation (further generalizations?---feature request)
- From: David Reiss <dbreiss at gmail.com>
- Date: Sat, 17 Apr 2010 06:06:25 -0400 (EDT)
- References: <hq414o$3cd$1@smc.vnet.net> <hq61q7$3i8$1@smc.vnet.net>
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 the Pade Approximant function that would be very > > useful would be the generalized Pade Approximant: these are Pade > > Approximants that are based on more than one expansion point. I coded > > 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 something > > 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 and have > been really impressed at the accuracy of the approach. > > > > According to Wikipedia: > > > > A Pad=E9 approximant approximates a function in one variable. An > > > 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 > used Pade at 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 are > 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 in 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-Engineers/dp/0387989315 --David