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MathGroup Archive 2006

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Re: Mathematica "Interpolation" function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71749] Re: [mg71630] Mathematica "Interpolation" function
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Tue, 28 Nov 2006 06:04:03 -0500 (EST)
  • References: <200611251037.FAA15639@smc.vnet.net>

Lorents wrote:
> Hello,
> I'm trying to understand how mathematica produces interpolations in 1D 
> with the "Interpolation" command. I understood it uses piecewise 
> polynomial of the degree specified by InterpolationOrder.
> As far as I understand this method never produces truly smooth functions 
> as nothing is done to elimitate the jump discontinuities in the 
> derivatives of the joined polynomials.
> Iimagine that these discontinuities may be small, but they are 
> nontheless there.
> Could anybody confirm this? Am I correct?
> 
> Lorenzo

Yes, you are correct.

Use of polynomials, or for that matter any basis of analytic functions, 
will result in failure of smoothness to some extent. This is true both 
for interpolation and splining.

Daniel Lichtblau
Wolfram Research


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