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Pade Approximation (further generalizations?---feature request)
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telefunkenvf14
Apr 14, 2010, 5:16:08 AM4/14/10
to
I've been playing around with PadeApproximant[] in Mathematica and have been
really impressed at the accuracy of the approach.
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
David Reiss
Apr 14, 2010, 11:39:51 PM4/14/10
to
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...):
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
--David
http://scientificarts.com/worklife
On Apr 14, 5:16 am, telefunkenvf14 <rgo...@gmail.com> wrote:
> I've been playing around with PadeApproximant[] in Mathematica and have b=
telefunkenvf14
Apr 16, 2010, 5:49:02 AM4/16/10
to
On Apr 14, 10:39 pm, David Reiss <dbre...@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> > I've been playing around with PadeApproximant[] in Mathematica and have=> 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
>
b=
> een
> > 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
David Reiss
Apr 17, 2010, 6:05:31 AM4/17/10
to
On Apr 16, 5:49 am, telefunkenvf14 <rgo...@gmail.com> wrote:
> On Apr 14, 10:39 pm, David Reiss <dbre...@gmail.com> wrote:
>
>
>
>
>
> On Apr 14, 10:39 pm, David Reiss <dbre...@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> > 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
>
>
> > On Apr 14, 5:16 am, telefunkenvf14 <rgo...@gmail.com> wrote:
>
> > > I've been playing around with PadeApproximant[] in Mathematica and have
>
> > > 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
> 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
David Reiss
Apr 18, 2010, 5:58:56 AM4/18/10
to
On Apr 17, 6:05 am, David Reiss <dbre...@gmail.com> wrote:
> On Apr 16, 5:49 am, telefunkenvf14 <rgo...@gmail.com> wrote:
>
>
>
>
>
> > On Apr 14, 10:39 pm, David Reiss <dbre...@gmail.com> wrote:
>
> On Apr 16, 5:49 am, telefunkenvf14 <rgo...@gmail.com> wrote:
>
>
>
>
>
> > On Apr 14, 10:39 pm, David Reiss <dbre...@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> > > > I've been playing around with PadeApproximant[] in Mathematica and => > > 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
>
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 i=> > 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
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:
>
>
> --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....
telefunkenvf14
Apr 28, 2010, 6:59:42 AM4/28/10
to
On Apr 18, 4:58 am, David Reiss <dbre...@gmail.com> wrote:
> On Apr 17, 6:05 am, David Reiss <dbre...@gmail.com> wrote:
>
>
>
> > On Apr 16, 5:49 am, telefunkenvf14 <rgo...@gmail.com> wrote:
>
> > > On Apr 14, 10:39 pm, David Reiss <dbre...@gmail.com> wrote:
>
> > > > Another addition to thePadeApproximant function that would be very> On Apr 17, 6:05 am, David Reiss <dbre...@gmail.com> wrote:
>
>
>
> > On Apr 16, 5:49 am, telefunkenvf14 <rgo...@gmail.com> wrote:
>
> > > On Apr 14, 10:39 pm, David Reiss <dbre...@gmail.com> wrote:
>
> > > > useful would be the generalizedPadeApproximant: these arePade
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
>
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
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.
>
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
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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