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Preference: approx clamped vs natural cubic spline


What are examples of some circumstances when we would prefer approx clamped and natural cubic spline?

I also assume that neither is preferable if we are given an additional 2 Ys (in that case we would use clamped cubic spline)

And since MATLAB uses not a knot by default, it is probably better (either computationally or because of some other properties)

However, not much is told about approx clamped and free/natural cubic spline.


Natural cubic spline gives the least curvature.
So if the design we want to do, requires fairly flat lines,
then natural is the choice.
Usually, (exact) clamped is a little more accurate
than approximate clamped, and the latter a little more accurate
than not-a-knot. But the differences are minor,
and not in the order of convergence, but just the actual error,
and close to the endpoints.