ON INTERPOLATION BY ALMOST TRIGONOMETRIC SPLINES

Sergey I. Novikov     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russian Federation)

Abstract


The existence and uniqueness of an interpolating periodic spline defined on an equidistant mesh by the linear differential operator \({\cal L}_{2n+2}(D)=D^{2}(D^{2}+1^{2})(D^{2}+2^{2})\cdots (D^{2}+n^{2})\) with \(n\in\mathbb{N}\) are reproved under the final restriction on the step of the mesh. Under the same restriction, sharp estimates of the error of approximation by such interpolating periodic splines are obtained.


Keywords


Splines, Interpolation, Approximation, Linear differential operator.

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References


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DOI: http://dx.doi.org/10.15826/umj.2017.2.009

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