Showing the simplifications that can be made if the points are evenly spaced.

If we write the order n-1 polynomial as the system
, where
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M is the nxn matrix of the abscissae (x-values of the tabular points),

x is the vector of unknown coefficients

y the y-values at the given abscissae
Then the Coefficients x are given by
If the points are equally spaced, for a given order n, the matrix M is constant. It can be calculated once, and used for all curves of the same order. By choosing n odd, and taking the midpoint of the interval as the zero point, the matrix can be further simplified.