Find the best fit 2 piecewise polynomial function for a data set with 1 optimal breakpoint location
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I have a 2D data set (2 variables x and y). I would like to use 2 piecewise polynomial functions with 1 breakpoint to best fit the dataset.
For example, function 1 = polynomial1 for mini_data < t < a and function 2 = polynomial2 for a<t<max_data. Also, I need to find the optimal breakpoint a value.
What maths tool/algorithm should I use, please?
Thanks in advance!
3 Comments
Torsten
on 26 May 2021
Edited: Torsten
on 26 May 2021
min: sum_{i=1}^{i=ndata} (p(xdata(i),a) - ydata(i))^2
subject to
p1(a,a) = p2(a,a)
p1'(a,a) = p2'(a,a)
xdata(1) <= a <= xdata(ndata)
with
p(x,a) = p1(x,a) for x<=a
p(x,a) = p2(x,a) for x>=a
Parameters to be optimized are a and the coefficients of the polynomials p1 and p2.
A typical application for Matlab's "fmincon".
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