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

From: Brian Gough
Subject: Re: [Help-gsl] The spline polynomial coefficients are unique (????)
Date: Fri, 20 May 2005 19:00:41 +0100

Athanasios Anastasiou writes:
 > 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.
 > 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 :-?

Most likely explanation is a difference in how the boundary conditions
are handled or an error in the GSL tridiagonal solver (certainly possible).

I wouldn't expect numerical error to be significant.

I would look at the difference in the solutions of the tridiagonal
system before looking at the interpolated results. The matrix solutions
should be pretty close.

 > 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).

For a standard spline, the tridiagonal system has to be solved, I
think--it depends globally on the data.

Brian Gough

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