Finding Zeros in 3D Data Set with GSL

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A user is seeking an effective root-finding method for a dataset of 3D points (x, y, z) where z = f(x, y), specifically looking for the zeros of the function f. They express interest in interpolation methods to accurately locate these zeros, rather than simply identifying where z equals zero or where sign changes occur. The discussion highlights that the choice of method depends on the assumptions about the data, suggesting options like linear, quadratic, or cubic fits. A recommendation is made for CurveExpert, a free software that performs these tasks effectively. Additionally, a resource on using the GNU Scientific Library (GSL) for interpolation is provided, which ranks highly in search results for GSL interpolation.
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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...
 
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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.
 
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.
 
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.
 
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