Optimization of energy functional for variational splines

The aim of this paper is to suggest optimization procedure for the refinement of energy functional in variational spline approximation problem. Our approach is based on a separation of measurement data between two sets. First is the set of basic measurements (nodes of spline), second is the set of control measurements (additional points). Additional data provides the reasonable choice of parameters in energy functional and may be the refinement of coefficients in mathematical model of the process we need to study.

The formulation of optimization problem in general form and example for Dm-splines with a tension are presented. Also the numerical algorithm of Newton's type is described.