Numerical methods to find parameter set with N intersections of 2 implicit functions

  • Thread starter Dovetailed
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Sorry for the wordiness of the thread title.

Basically I'm wondering, if you have two implicit functions, F(x,y)=0 and G(x,y)=0 (typically rational functions with numerator and denominator very high degree polynomials), both dependent upon the same K (in my case > 34) dimensional set of parameters - a for i = 1 to K; are there any established numerical techniques to speed up a search of the parameter space to find a set of parameters for which the 2 curves in the x-y plane (defined by the functions F and G) have a given number of intersections, say N?

Cheers!
 

fresh_42

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You can apply algebraic geometry to some extent, but this depends on many things you haven't said. But algebraic geometry would be the direction in which I sought.
 

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