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## Re: [Help-gsl] The spline polynomial coefficients are unique (????)

 From: Athanasios Anastasiou Subject: Re: [Help-gsl] The spline polynomial coefficients are unique (????) Date: Tue, 17 May 2005 22:06:20 +0100 User-agent: Mozilla Thunderbird 1.0 (X11/20041206)

```Dear Brian

Thank you for replying to my message.

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Well, i have done the same thing that you are suggesting but using MATLAB, testing the output of my implementation at different stages.
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In the case of long and very long time series interpolations (more than 15 and more than 500 x,y pairs respectively) there are errors only in the begining and at the end of the interpolation.
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The only source of errors i can think of would be round off errors at the stage of the solution of the tridiagonal system and the calculations that follow this to derive the rest of the coefficients. But then again the rest of the coefficients should have some error :-?
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I have selected the implementation where a tridiagonal system of equations is set up and solved and from this solution all the rest of the coefficients are derived.. However, i ran on a site today and there was an algorithm in pseudocode which did not set up a system of equations at all and it did not look like a recursive based method too. Any more information on that? (It was odd because every implementation i have seen so far uses a linear system of some sort).
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All the best.
thanOS

Brian Gough wrote:

```
```Athanasios Anastasiou writes:
> The problem is that i get three different implementations for three
> different spline interpolation "providers" and honestly i dont know
> which one to assume true!!! (so much for the uniqueness of the polyonym
> :-) [only joking])

Hell,

I would suggest using GNU octave to generate the matrix from the
recurrence relations and solve it, then you can see at what stage the
discrepancy arises (by looking at the intermediate results in GSL with
gdb, for example).

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```

```