curve fitting

I cheated, used CurveExpert to sort thru functions.

Taking the log of H yielded a fairly good fit over most of the range; the very high end has a problem

If you take the log of the H.I values then a polynomial gives a reasonable fit, but a rational polynomial gives a better fit, with fewer terms.

Or you could use spline interpolation.

wander perez sena wrote: i found somes examples in here and i tried to used them with my data and they didnt work.

You would have to be more specific if you'd like to receive some help on this and provide the examples and what you did which did not work.

i got this data that represents a curve and i want to find a function,

Do you need an analytic function or would a piecewise interpolation would do the job as well? Or are you in need for a regression function (of which type?)?

maybe a Lagrange interpolating polynomials that fits this data

Hmm, this would be a polynomial of order 63 and sure suffers from some bad oscillations. Wouldn't recommend using it:

If interpolation is all you are asking for, you basically have the choice between simple linear interpolation (see attached file) or cubic splines:

If you are in need for an analytic function you would resort to an approximation by regression. Playing around and trying various function types, I, too, found, that a rational polynomial gives the best fit so far. But Richards approach of fitting the log data with a rational of higher degrees polynomials gives you an even better fit.

Regards

Werner