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

[Raymond Rogers]

Thanks for the clarification.  There are several other ways to approach
that; but without knowledge of the application there is no way to choose.

On Mon, Nov 30, 2015, 8:49 PM Patrick Alken <address@hidden> wrote:

> 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> 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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>