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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


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