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MathGroup Archive 2000

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Re: [TS 3227] ListInterpolation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23527] Re: [mg23467] [TS 3227] ListInterpolation
  • From: "William F. Campbell" <valentin at wam.umd.edu>
  • Date: Tue, 16 May 2000 22:29:58 -0400 (EDT)
  • Organization: UMD Dept. of Meteorology
  • References: <8figbj$4r8@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Interpolation doesn't implement smoothness constraints.  Suppose you
call Interpolation[data,InterpolationOrder->3].  Mathematica gives a cubic fit
to points 1 through 4, then another cubic from 4 through 7, then
another from 7 through 10, etc.
In other words, if you call Interpolation[data,InterpolationOrder->3],
you get cubic curves, but NOT cubic splines, which is what I think you
want.
I have a fairly ugly and inelegant cubic splines routine for
Mathematica, but it does work, and produces smooth interpolation.  If
you are interested, send me email, and I'll send it to you

Bill Campbell

> "Interpolation works by fitting polynomial curves between successive data
> points. "
> 
> In other words, the curve pases through each data point input.  If you have many
> data points, you probably need to increase the PlotPoints to see the noise in
> your original data.
> 
> As for the derivatives, I have the same problem with my data.  A smoothing
> routine that would accurately represent the major trends without the in-between
> small variances would be nice.


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