In this paper, we provide an interpretation of polynomial spline interpolation as a continuous filtering process. We prove that the frequency responses of the cardinal spline filters converge to the ideal lowpass filter in all L f n o r m s with 1 ~<p < + ~ as the order of the spline tends to infinity. We provide estimates for the resolution errors and the interpolation errors of the various fi...

In [4] the first named author discussed the explicit solutions of the cubic spline interpolation problems. We are now concerned with quintic spline functions. Let 5B[0, n] denote the class of quintic spline functions S(x) defined in the interval [0, n] and having the points 0, 1, • • • , n — 1 as knots. This means that the restriction of S(x) to the interval (*>, J > + 1 ) (P = 0, • • • , n — \...