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Re: BUG or FEATURE in Interpolation[] ?

• To: mathgroup at smc.vnet.net
• Subject: [mg4632] Re: BUG or FEATURE in Interpolation[] ?
• From: Harald Berndt <haraldb at nature.berkeley.edu>
• Date: Thu, 22 Aug 1996 03:54:51 -0400
• Organization: University of California Forest Products Lab
• Sender: owner-wri-mathgroup at wolfram.com

Stefan Schulz wrote:
> ...
> I found to my surprise, that the function returned by Interpolation
> is not smooth at some of the data points!

Well, it is documented: The Book says that the approximated function 
varies smoothly between sample points, nothing about smoothness of 
derivatives at sample points. And if you set InterpolationOrder -> 1, 
you get just plain linear interpolation.

>For this reason I resorted to
> write a package Spline1D which returns a smooth cubic spline as a
> pure function, but is naturally slower than the built-in Interpolation
> command.

You could probably have used the "Graphics`Spline`" standard package.

>Did I find a bug or is this a feature? If it is a feature
> it certainly makes the Interpolation command not suitable to obtain
> smooth curves.

There's also InterpolatingPolynomial (which returns something you 
probably don't want in your particular example) and of course Fit[] or 
NonlinearFit[].

-- 
_______________________________________________________________
Harald Berndt                          University of California
Research Specialist                  Forest Products Laboratory
Phone: 510-215-4224                            FAX:510-215-4299
_______________________________________________________________



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