A class of cubic splines obtained through minimum conditions

Source abstract

A class of cubic spline minimizing some special functional is investigated. This class is determined by the solution of a quadratic programming problem in which the minimizing function depends linearly on a parameter α > 2 \alpha > 2 . For α = 1 / 2 \alpha = 1/2 natural splines are obtained. For α = − 1 \alpha = - 1 the spline minimizing the mean value of the third derivative is obtained. It is shown that this spline has the best convergence order.