in reply to Estimating continuous functions
As I understand it, this is generally considered a "doozy" of a problem. You have to accept the fact, that for any sets of points, there are an infinte number of curves that fit them, and except in simple cases, there's usually no way to determine that one curve is "more correct" then another -- and in the really simple cases, it's even worse (consider the points where y=cos(x) and y=sin(x) intersect, then consider how man even simpler curves all go through the same points).
There do however seem to be a few papers online that discuss how you can approximate it if you're willing to make ceratin assumptions. The math is way over my head, but knock yourself out...