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I have pairs of data arrays (say x_n and y_n), which represent some result y_n(x) that converges with n.

-These arrays become more densely populated for larger n.

-There are no common elements in any x_n arrays.

-The data itself cannot be fitted.

-I have pairs of these arrays for several values of n (but not too many).

-Visually there seems to be good convergence, maybe a power law.

Can I estimate a converged result (again as a pair of arrays to be plotted) based on the numerical data that I have? I was wondering whether there is a method/library in python that would help with this?

lightfield
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  • You said the data cannot be fitted but you want to estimate a convergence result? If I am understanding correctly, you are trying to find a best fit plot. I would assume you do a [polynomial best fit curve with numpy](https://numpy.org/doc/stable/reference/generated/numpy.polyfit.html) – Daniel me Oct 29 '21 at 23:13
  • Each curve y vs. x cannot be fitted but when many of these curves are plotted for different n there is a convergence (polynomial with n) towards the exact curve which I want to estimate. Since I have only numerical data (no x-values in common and I am wary of interpolating), it is not straightforward how to approach this and whether this can be done at all. I am interested if there are some more specialist numerically based methods/ (third-party) libraries in Python that may help. – lightfield Oct 30 '21 at 12:28

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