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MathGroup Archive 1996

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Re: Expl. form of Interpolation[] ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg3680] Re: Expl. form of Interpolation[] ?
  • From: Robert Knapp <rknapp>
  • Date: Fri, 5 Apr 1996 02:52:45 -0500
  • Organization: Wolfram Research, Inc.
  • Sender: owner-wri-mathgroup at wolfram.com

Manfred Krafczyk wrote:
> 
> Dear All,
> given a set of points in list={y1,y2,...,yk} one can use
> f=Interpolation[list] to get an implicit interpolation function
> which can be plotted etc., but I did not find out how
> to get the explicit polynomial f[x] which is implicitely generated
> and used by calling f[x] (i.e. the coefficients
> of the powers in 'x') in order to port this algebraic
> expression into a C code for further use.
> Any ideas welcome (preferably e-mail),
> Thanks in advance
> Manfred Krafczyk

The InterpolatingFunction produced by Interpolation does not use a
single polynomial.  It uses a piecewise (default 3rd order) polynomial
approximation.  It is possible to obtain the coefficients using the
InterpolatingPolynomial function.  Since InterpolatingPolynomial does
not use a piecewise approximation, if you want a piecewise
approximation, it will be necessary to partition you interval in
sections: you can use Partition and Map to do this realtively easily.

-- 
Rob Knapp
Wolfram Research, Inc.

http://www.wri.com/~rknapp

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