My question is simple: is it possible to calculate the local maximums and minimums for data fitted with a natural cubic spline? If yes, how would I approach this problem?
I work on large genome wide datasets, and my hope was to fit polynomial functions to several 1000 regions of my data, and the look for patterns by comparing the polynomials. However, the regions of interest are too large for a simple polynomial, so I have attempted to use splines. Now I am running into problems computing local minimums and maximums for the splines.
Any help or hints would be appreciated, including an approach other than splines. Although lagrange interpolation, even with regularization, didn't do the trick.