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I have a set of real-world data points that I wanted to find a curve for, to help with additional numbers. I plotted them on a graph using desmos and can get a decent approximation of what values would be alone the curve. I thought I'd run a Lagrange interpolation using DCode to find the formula, but it created a bumpy ultra-specific tangent-like curve while I was expecting a smooth log-like curve. :) This might be due to noise in the real world data, of course.

https://www.desmos.com/calculator/dyxtcmpgtf <-- probably not the curve I'm looking for :)

Anyway, just thought I'd throw it out there to y'all in case you have a better process. Or, just confirm to me that it's an impossible task!

John K. Addis
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  • From where do you have the data? Do you have any prior on the data? I mean real-world data points can come from anywhere and without any other requirement or knowledge it is difficult to find any good (or rather meaningful) approximation. You can think of it as a very ill-posed inverse problem, which is basically impossible to "solve". – CostaZach Sep 10 '20 at 15:48
  • Try polynomial regressions (in python). –  Sep 10 '20 at 18:24
  • You can fit an exponential, e.g, $e^{\lambda x}$ to the data (by minimizing mean square error, etc) in which case for the given data $\lambda<0$. Google sheets actually has a built in function for this. Or you could use splines, in particular cubic splines as they have the best balance of accuracy and efficiency. – K.defaoite Sep 11 '20 at 14:33
  • Do you have more datapoints? – an4s Sep 11 '20 at 15:29
  • You can try some more fits as shown here. – an4s Sep 11 '20 at 15:36

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