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I am looking for a procedure with Mathematica where one can discretize a function in a specific interval to a set of multidimensional vectors. In this way, we can possibly ease the calculation time required to work with these long functions. All I could find on Mathematica is https://reference.wolfram.com/language/ref/DiscretizeRegion.html but this is not relevant.

To get an idea of the complexity of these functions, the functions are shown here

https://www.wolframcloud.com/obj/2abadd04-3d65-4f29-bd8c-e847f1607ef4

Thanks

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    $\begingroup$ You could use 'Table' to sample the function at regular intervals. Something like 'Table[{x,d[x]},{x,-1,1,inc}]' . The issue would be to choose a value for inc that is small enough for what you need. This is related to the highest frequency of interest in your time history. Am I along the correct lines? After sampling then you could use 'Partition' to seperete into subintervals. $\endgroup$
    – Hugh
    May 17, 2023 at 11:52
  • $\begingroup$ I believe you're looking for the term "interpolation" instead of "discretization", perhaps? $\endgroup$
    – Michael E2
    May 17, 2023 at 14:10
  • $\begingroup$ @Hugh, exactly. This is what I was looking for... The aim is to find a minima between the discretized functions there, and another set of related discretized functions. Then use these minima to solve the system of equations that give a Gaussian function with 4 unknowns. $\endgroup$ May 17, 2023 at 16:04

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This is one way to do it:

fi = FunctionInterpolation[g[x], {x, -3, 3}]
Plot[fi[x], {x, -3, 3}]
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