On An Interpolation of a Function by Exponential-Trigonometric Natural Splines

ne of the challenges in approximation is the interpolation problem. Splines are often used for function approximation. The theory of splines includes both algebraic and variational approaches. In both cases, the existence, uniqueness, and convergence of splines, along with algorithms for their construction, are studied based on their inherent properties. In this paper, we study the problem of constructing exponential, exponential-trigonometric natural splines in the Hilbert space W(m;0) 2 (0; 1). Here, using the Sobolev method, we present an algorithm for solving a system of linear algebraic equations for the coefficients of natural splines. For m = 1 and m = 3, we obtain explicit expressions for the coefficients of natural splines in the Hilbert spaces W(1;0) 2 (0; 1) and W(3;0) 2 (0; 1).