Coefficients for a Series of Known Functions

  One can generalize the least squares fit for a Taylor series by replacing the functions x^p with an arbitrary set of functions f_p(x). The set of functions could be the sines and cosines of a Fourier series for example. The derivation is much the same as before but one can see the advantage of using the dot products for the correlations. The components of the f_p vectors are f_p(x_k) for each x_k in the dataset.