Given nite subset J IR n , and a point 2 IR n , we study in this paper the possible convergence, as h ! 0, of the coeecients in least-squares approximation to f(+hh) from the space spanned by (f(+ hj) j2J. We invoke thèleast solution of the polynomial interpolation problem' to show that the coeecient do converge for a generic J and , provided that the underlying function f is suuciently smooth....