WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 25, 2026
Smooth Polynomial and Non-polynomial Splines of the Second Order of Approximation
Authors: ,
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Abstract: Continuous local polynomial splines are widely used in approximations, as well as in solving differential and integral equations.. In this paper, we consider the construction of continuously differentiable splines of the second-order of approximation. We construct continuously differentiable polynomial and non-polynomial splines by smoothing continuous local approximations. The construction of smoothed non-polynomial approximations is discussed using the example of constructing smooth trigonometric splines. Theoretical results are given. Results with numerical experiments are presented. Among the numerical experiments, the approximation on a non-uniform grid of nodes is considered, as well as the influence of introducing additional errors into the values of the function given at the grid nodes.
Keywords:
polynomial splines, non-polynomial splines, smooth approximations, continuous local approximations, interpolation, trigonometric splines
Pages: 481-494
DOI: 10.37394/23202.2026.25.38