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Preference: approx clamped vs natural cubic spline


#1

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.


#2

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.