Algorithms of calculating of approximating spline functions with optimization of the location of spline nodes

The problem of computing spline approximation functions taking into account the possibility of optimizing the location of spline nodes is considered. Algorithms are developed to compute spline approximation functions with free conditions at the ends of observation intervals, with controlling of splines by the zero and first derivatives at the ends of observation intervals, and with the provision of optimal locations of spline nodes. The results of mathematical modeling of the algorithms for computing spline approximation functions are presented.