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Show with a simple example what is the difference between interpolation and extrapolation?




I find it difficult to understand the math methods. analysis through reference books. Did I understand correctly in the most general sense what interpolation and extrapolation are:

interpolator = (array [i] + array [i + 1]) / 2;
then we put it between array [i] and array [i + 1];
extrapolator = (array [i-2] + array [i-1] / 2);
and we put it in place of array [i].

I sketched the code myself, as best I could .. As the most primitive way to approximate the values ​​of points, I chose the arithmetic mean between them ..

Answer 1, authority 100%

Interpolation is finding an intermediate value between two known ones, according to some algorithm. Your example is generally correct:

// For example, the arithmetic mean:
interpolator = (array [i] + array [i + 1]) / 2;
// Place between array [i] and array [i + 1]

Extrapolation , this is finding the next value from the known previous ones, according to some algorithm. The most common example would be like this:

// For example, a linear continuation over the last 2 points:
extrapolator = (array [i-1] + (array [i-1] - array [i-2]));
// Place array [i] in place

Algorithms can be very diverse, from repetition of values, to curve fitting, etc. In general, the algorithms may be similar, but extrapolation is usually more algorithmically complex.

P.S. enter image description here

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