How to fit ascending data with piecewise linear function?

Hi, I have a vector r sorted in asending order. Now I would like to fit this r with m+1 pieces, and extract the m internal points.

E.g, my data is:

r = [1,1.5,1.6,2,3,3.1,3.2,3.5]

If m = 2, then I can fit three lines to r, and the internal points are [2,3].

Is there a way to do this algorithmatically?

Thank you very much.

[Mathieu NOE]

hello

could you please clarify what is your intention ? the internal points are supposed to correspond to the integer values in your data vector or what is the logic to choose which values are meaningfull in your linear piecewise interpolation ?

Answer 1

[Matt J]

There are some spline fitting tools on the file exchange that would be applicable:

https://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling

https://www.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation

Note that a piecewise linear function is a first-order spline.