Cubic Spline Interpolation versus Interpolating Polynomial

Given equally spaced sample values of a function , one can approximate as the polynomial of degree that passes through all points on a plot. Runge's phenomenon tells us that such an approximation often has large oscillations near the ends of the interpolating interval. On the other hand, cubic spline interpolation is often considered a better approximation method because it is not prone to such oscillations. However, if the sample rate is sufficiently high relative to highest frequency in the signal, then an interpolating polynomial has a smaller approximation error than a cubic spline interpolation.