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MathGroup Archive 2006

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Re: Mathematica "Interpolation" function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72015] Re: Mathematica "Interpolation" function
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Fri, 8 Dec 2006 06:18:05 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <ek98a7$jpi$1@smc.vnet.net>

In article <ek98a7$jpi$1 at smc.vnet.net>, Lorents <lorenzo at amp.fi> wrote:

> 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.

Yes -- but note that if you know any derivatives you can pass them to 
Interpolation. From the online help:

 Data can be given in the form {{x1, {f1, df1, ddf1, ...}, ...} to 
 specify derivatives as well as values of the function at the points xi. 
 You can specify different numbers of derivatives at different points. 

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)    
AUSTRALIA                               http://physics.uwa.edu.au/~paul


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