I'm analyzing financial data and would like to find the inflection points of a line. I know I can do this using derivatives, but first I need an equation. Is there a way to generate an equation based off of a series of numbers. I would need to do this programmaticly.
Spline interpolation is probably more useful for you than polynomial interpolation: if you fit a polynomial, it must inevitably head off to +/- infinity outside your data range.
You will also want a method which allows a slightly loose fit: financial data is often a bit noisy which can result in very weird curves if you try to fit it exactly.