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I've got a set of data that's been manipulated solely numerically. But anyway, for a certain part of that data set, I see that it's convergent (image). But I'm sort of at a loss for how depict that convergence with say, a table, because the error oscillates chaotically but is clearly heading to zero.

enter image description here

Comparing the next error to the previous one will at some points show an increase in the error. I was thinking of using an averaging technique (e.g. Simpson's Integration) which allows me to "smooth out" the curve if I do it enough times. I just don't know if that's a valid approach.

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I can think of a few approaches to your situation:

  • Use a moving average or other smoothing technique. However, there are better approaches than numerical integration, e.g., using a kernel smoother. (Simpson’s method is almost certainly not the best choice.)

  • Fit a model function for the decay to the data, e.g., at first glance, yours looks like an exponential decay. This makes more sense if you have some theoretical reason to assume a specific shape of the decay.

  • As your data is numeric: Average over several realisations for each choice of the control parameter.

You have to decide yourself which of these approaches makes sense and is feasible for your situation.

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