Re: [Bug-gsl] What I am doing wrong / gsl_interp_polynomial

[Patrick Alken]

He's interpolating, not least-squares fitting. Therefore to interpolate
N points he needs a polynomial of degree N-1. A least squares approach
might be better since he could interpolate his 1000 points with a much
lower degree polynomial, say 6 or 7.

On 11/30/2015 05:22 PM, Raymond Rogers wrote:
>
> Are you sure you aren't fitting noise?  This results in oscillation
> due instantaneous fluctuations shoving high frequency into the model.
>
>
> On Mon, Nov 30, 2015, 6:58 PM Patrick Alken <address@hidden
> <mailto:address@hidden>> wrote:
>
>     Hello,
>
>        I confirmed that your program is failing for the polynomial
>     interpolation, but polynomial interpolation is known to be
>     difficult for
>     large datasets. From the manual:
>
>     ====
>     Interpolation Type: gsl_interp_polynomial
>
>          Polynomial interpolation. This method should only be used for
>     interpolating small numbers of points because polynomial interpolation
>     introduces large oscillations, even for well-behaved datasets. The
>     number of terms in the interpolating polynomial is equal to the number
>     of points.
>     ====
>
>     So basically you are trying to fit a degree 1000 polynomial to your
>     dataset, which will not be numerically stable - even though your
>     dataset
>     is well behaved.
>
>     Cubic splines are probably the way to go here, but if you insist on a
>     degree 1000 polynomial (even though you shouldn't) I might be able to
>     give you some further ideas.
>
>     You mentioned that previous versions of GSL worked for you. Can you
>     verify if you used exactly this same dataset successfully with a
>     previous version of GSL? If so please tell me the version number.
>
>     Thanks,
>     Patrick
>
>     On 11/30/2015 10:25 AM, Petrus, Adam (UK) wrote:
>     > I am attempting to use the polynomial interpolation method with
>     GSL. However I am getting very strange results.
>     >
>     > If I run the attached program I get the below result. If I
>     change the method to linear or cspline the interpolation works fine.
>     >
>     > Not in previous gsl versions the polynomial interpolation has
>     worked!
>     >
>     > [cid:image001.png@01D12B93.B5E118F0]
>     >
>     > Is there something I am missing?
>     >
>     > Yours aye
>     >
>     > Adam
>     >
>     >
>     >
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