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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


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