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Omer Saglam on 8 Jun 2020
Commented: John D'Errico on 10 Jun 2020
This question was flagged by Rik

Rik on 8 Jun 2020
Why did you write it on a piece of paper? Now it is difficult to suggest edits.
Rik on 10 Jun 2020
Natural Cubic Spline Interpolation Choose x0, x1, x2, x3 and y0, y1, y2, y3.
Write an .m file to compute the third order polynomials for the intervals [x0, x1], [x1, x2], [x2, x3]. Plot the functions and the points xi, yi on the same figure. Figure should clearly show that the polynomials pass through the points.
I will choose my own xi, yi and test your code
John D'Errico on 10 Jun 2020
What do I think of that solution? It reminds me vaguely of a comic that I recall hanging on every office wall, in every breakroom where I worked and went to school.
It showed two scientists discussing some scribbles on a blackboard. A theorem perhaps. But in the middle of those scribbles with the derivation is a cloud that contains the words "and then a miracle occurs".
Effectively, your solution of a cubic spline also requires a miracle. The flow chart before and after that seems not unreasonable. Some things probably need to be filled out. But it is that miraculous cloudy part that will be the hang up.

Ameer Hamza on 8 Jun 2020
Edited: Ameer Hamza on 8 Jun 2020
See interp1(): https://www.mathworks.com/help/releases/R2020a/matlab/ref/interp1.html with 'pchip', or 'spline' methods.