Math::Polynomial has methods of creating such functions.

Specifically, Math::Polynomial::interpolate. It may not be such a good idea to fit your entire data set with a polynomial and then maximize it. For one, it can be slow. For two, the high-order polynomials found by fitting many points show a lot of "stiffness" which makes them bad for fitting unsmooth functions (where "smooth" is defined as "similar to a polynomial") -- whether this is a problem for you depends on your data set. Be careful with Brent's method, also, because it can get stuck in a local maximum.

For quadratic interpolation, you can take the maximum data point and its two neighbors and fit them with Math::Polynomial. You can easily find the maximum of the resulting parabola by setting the derivative equal to zero. No need to use Math::Brent.

Update: I realized that I was confused between regression and interpolation right after hitting submit. Quadratic regression, as demontrated by tall_man, is probably a good idea if your data is all fairly close to the peak.

In reply to Re: Re: mathsy question by no_slogan
in thread mathsy question: finding max of curve from discrete points by Anonymous Monk

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