Re: Why this is so difficult to do curve fitting?

From: Uwe Schmitt (schmitt_at_num.uni-sb.de)
Date: 08/16/04 

Date: Mon, 16 Aug 2004 17:42:07 +0200

>
> take a look at polynomial interpolation.The solution might not be of
> the form y = a*(x/255).^b+ c ,but might fit the data more accurately
>
>
> http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html
>
> ram

I do not think that this is a good idea. Interpolating the given
data requires a polynomial of degree seven. Interpolating gets
very unstable for degrees greater four, that is: minimal change
of the data leads to big derivations in the coefficients of
the fitting polynomial and thus big derivations if evaluating
this polynomial.
Especially as lucy asks for fitting, I assume that the given
data are noisy and that it is not assumed that the searched for
function exactly hits the given 2d points.

Greetings, Uwe.