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Topic: Which interpolation?
Replies: 4   Last Post: Dec 10, 2012 12:22 PM

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Dave Dodson

Posts: 690
Registered: 12/13/04
Re: Which interpolation?
Posted: Dec 7, 2012 3:48 PM
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The data presented suggest that the function has a horizontal asymptote at y = 1. If you expect that this is the case, you should try a model that has such an asymptote. E.g., y(x) = 1 + a/x + b/x^2 + ... or y(x) = A*exp(-a*x) + B*exp(-b*x) + ....

Dave

On Friday, December 7, 2012 12:13:12 PM UTC-6, Cristiano wrote:
> From a very slow simulation I got y= f(x):
>
> x y
>
> 5 0.8048174
>
> 6 0.8194384
>
> ...
>
> 44 0.9706268
>
> 47 0.9724846
>
> ...
>
> 48765 0.9999756
>
> 53765 0.9999776
>
>
>
> For every x, I stop the simulation when the confidence interval for y is
>
> less than 2,5*10^-6 (with 99% of confidence).
>
>
>
> I can't calculate all the x's (because the simulation is very slow), so
>
> I need to interpolate; for example, I don't have y(45) or y(46).
>
>
>
> Using the Levenberg-Marquardt Least Squares Fitting, the best equation I
>
> found gives an error that is too high (about 10^-4 for small x's).
>
>
>
> Then I thought to use a cubic spline, but I notice some "fluctuations"
>
> on the tails.
>
>
>
> Should I use LM or spline?
>
>
>
> Thanks
>
> Cristiano





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