"Математика. Компьютер. Образование". Cб. трудов XII международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2005. Vol. 2, 466pp. Pp. 593-605.
This paper considers application of special S-splines. These spline’s construction is based on condition of 1st derivative’s smoothness and on the method of least squares. Distinction of these splines is their semi-locality (i.e. every polynomial knows all the preceding function’s values and doesn’t know the following ones). Basic S-splines are constructed using these splines that give us an ability to consider any function as linear combination of basic splines. Basic splines are applied for function approximation, solving of differential equations (using method of Galerkin) and for getting a quadrature formulas. S-spline on circle is constructed in the same way that allows us to solve the same tasks for circle and for more complex areas.