What is the order of accuracy of the cubic spline interpolation method? I have been looking around but not sure if I am getting the right idea. Does it have fourth-order accuracy? How should one derive the result? Any references would be appreciated.
Thank you!
This is all covered in Carl de Boor’s book entitled “A Practical Guide to Splines”. Yes, the approximation is fourth order.
Or, see formula (1) in these notes.
Or look at the answers to this question.