Optimization of parameters for curve interpolation by cubic splines

In this paper, we present an interpolation method for curves from a data set by means of the optimization of the parameters of a quadratic functional in a space of parametric cubic spline functions. The existence and the uniqueness of this problem are shown. Moreover, a convergence result of the method is established in order to justify the method presented. The aforementioned functional involves some real non-negative parameters; the optimal parametric curve is obtained by the suitable optimization of these parameters. Finally, we analyze some numerical and graphical examples in order to show the efficiency of our method.