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From "J.Pietschmann" <j3322...@yahoo.de>
Subject Re: [Math 1.1-rc2] Neville and DividedDifference Interpolators... weird values????
Date Sun, 18 Dec 2005 21:06:02 GMT
vachevil-basic@yahoo.com wrote:
> We have a question about the results of the DividedDifferenceInterpolator and NevilleInterpolator
> as they seem to be very very out of line in comparison with the results of the SplineInterpolator.
...
> Vertex(X)  Value(Y)
> 2          4.6950
> 7          4.7550
> 14         4.7763
> 30         4.7938
> 60         7.4250
> 90         7.0688
> 120        4.6825
> 150        6.5438
> 180        4.6275
> 210        4.6050
> 240        4.5819
> 270        4.5575
> 310        4.5438
> 360        4.5313
> 
IIRC the Neville Algorithm will construct a single polynominal. With 14
values provided, the polynominal will have a degree of 13. Polynominals
of such a high degree have a tendency to oscillate wildly. It's not
really a surprise it will evaluate to negative values in your case.

This behaviour was BTW the major driver behind the invention of spline
interpolation.

J.Pietschmann

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