Zeros in a data set

[r4nd0m]

Hi,
does anyone know of some nice root-finding method (preferable GSL :-)) for a data set - i.e. I have a set of 3D data (x,y,z) where z = f(x,y,) and I want to know where the zeros of f are. I guess, I could write it myself with some interpolation method, but just in case someone knows...

 

[CRGreathouse]

If you have the function only in terms of triples, then the best you can do is search for:
1. Values of z which are actually equal to zero.
2. Sign changes from one value of z to the next.

 

[r4nd0m]

yeah, but I'd like to know where exactly the points are, so the method I'm searching for should be using some kind of interpolation and then find the zeros.

 

[CRGreathouse]

Ah. Well this depends on the assumptions you make about the data. You could do a linear (or quadratic, or cubic, or some other polynomial) local fit/spline, or you could choose any of a number of other types of fits.

There's a free ("as in beer") program out there called CurveExpert that does this reasonably well, if you'd like to try it.

 

[CRGreathouse]

I also see a page on using GSL for interpolation:
http://www.physics.ohio-state.edu/~ntg/780/handouts/gsl_interpolation.pdf

It was the Google result #1 for 'GSL interpolation'.