Sunday, April 21, 2013

Coefficients for a Series of Known Functions

  One can generalize the least squares fit for a Taylor series by replacing the functions xp with an arbitrary set of functions fp(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 fp vectors are fp(xk) for each xk in the dataset.

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