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MathGroup Archive 2006

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Re: Mathematica "Interpolation" function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71724] Re: Mathematica "Interpolation" function
  • From: dh <dh at metrohm.ch>
  • Date: Mon, 27 Nov 2006 04:05:07 -0500 (EST)
  • Organization: hispeed.ch
  • References: <ek98a7$jpi$1@smc.vnet.net>

Hi Lorenzo,
you are right. Consider an interpolation with default degree of 3:
d = Table[Random[], {10}];
f = Interpolation[d];
Plot[f[x], {x, 1, 10}];
Plot[f'[x], {x, 1, 10}];
You will see, that the first 3 points are calculated with one 
polynomial, the 3. and 4. with another, the 4. and 5. with still another 
e.t.c. This gives only C0 differentiability, already the first 
derivatives are not continuous.
Daniel

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
> 


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