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Re: Interpolation vs. SplineFit

• To: mathgroup at smc.vnet.net
• Subject: [mg21927] Re: [mg21889] Interpolation vs. SplineFit
• From: Bojan Bistrovic <bojanb at physics.odu.edu>
• Date: Fri, 4 Feb 2000 02:54:53 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

> 
> Hello-
> 
> What is the difference between a Cubic SplineFit and Interpolation with
> InterpolationOrder->3?  In the documentation, Interpolation works by fitting
> polynomials of the specified order over the data.  This is also the concept
> behind SplineFit.  When I have compared the two functions, the Interpolation
> function creates a "smoother" plot, however, it has some undesirable ripples.
> SplineFit more accurately interpolates the physical realities of the data, but
> cannot handle any data points outside the region of the original data set.  I
> would like to use Interpolation so that I can extrapolate beyond the original
> data range (carefully, of course).
> 
> Mostly, I'm interested in the differences in how SplineFit and Interpolation
> create functions over the data.
> 
> Thanks
> 
> Matt Johnson
> 
> 
Interpolation will always produce the function, and when I say function, I
mean in mathematical sense: for each "x" there's ONE AND ONLY ONE f[x]; spline
will fit it to a line in a plane, so for one "x" you can have more f[x]-es.
Look at NumericalMath`SplineFit` for examples.

Bojan

--
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Bojan Bistrovic,                       bojanb at physics.odu.edu  
Old Dominion University, Physics Department,      Norfolk, VA
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