In a post that already exists, implementation-of-monotone-cubic-interpolation, there is a good method for fitting data which necessarily includes all of the given points. But, what if I need to correct for some noise in a data set, and still preserve monotonicity? Is anyone familiar with a method of fitting data that provides a monotonic function that passes through the middle of a set of points, rather than each point individually?
In this case, the data points may not be monotonic to begin with, but because of knowledge of the system I know that a model of the data would have to increase continuously.
(Ultimately, I need to take numerical derivatives of some experimental data sets. The data are spaced far enough apart that it is necessary to interpolate points, or the derivative will have too large of delta x to be useful.)