Optimization of the parameters of surfaces by interpolating variational bicubic splines

In this paper we present an interpolation method from a surface or a data set by the optimization of a quadratic functional in a bicubic splines functional space. The existence and the uniqueness of the solution of this problem are shown and as well a convergence result of the method is established. The mentioned functional involves some real non negative parameters; the optimal surface is obtained by a suitable optimization of these parameters. Finally, we analyze some numerical and graphic examples in order to prove the efficiency of the presented method.