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

[Petrus, Adam (UK)]

Thanks for your prompt replies!

It is a general application where the user chooses the method of interpolation. 
I have modified it so if the user chooses the polynomial option and there is 
more than 64 points it now does not display the option or sets the method to 
spline. Thanks for the suggestion of the least squares approach.

Yours aye

Adam

From: Raymond Rogers [mailto:address@hidden
Sent: 01 December 2015 04:37
To: Patrick Alken; address@hidden; Petrus, Adam (UK)
Subject: Re: [Bug-gsl] What I am doing wrong / gsl_interp_polynomial


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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<mailto: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<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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