Whats the advantage of natural spline curve interpolation over polynomial fitting?
Polynomial fitting attempts to create one polynomial to represent the entire curve. The summary of the quadratic distances between the polynomial and the points is minimized. Depending on the polynomial’s degree the distances between polynomial and given points differs, for higher degree polynomials you typically have to expect oscillations. Natural spline interpolation constructs a sequence of cubic splines, hitting all the specified points. The distance between the interpolated curve and the given points is 0.
