Prove that, if the number m of functions f_j equals the number l of points (x^[k] , y^[k]), then the least squares solution [2.103] reduces to the interpolation solution [2.49]. In this regard, ordinary least squares is a generalization of ordinary interpolation.

Recall that, for nonsingular square matrices h and k:

[s1]

Solution [2.103] for ordinary least squares assumes that columns of f are linearly independent. If m = l, then f is a nonsingular square matrix. Applying [s1] to solution [2.103], we obtain:

[s2]

which is solution [2.49] for ordinary interpolation.