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

If we write the order n-1 polynomial as the system[br] [math]{\small A x = y } [/math], where[br] [list][br][*]M is the nxn matrix of the abscissae (x-values of the tabular points),[br][*] [b]x[/b] is the vector of unknown coefficients[br][*] [b]y[/b] the y-values at the given abscissae [br][br]Then the Coefficients [b]x[/b] are given by [math]{\small {\bf x} = M^{-1} {\bf y }} [/math][br][br]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.