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Polynomial and trigonometric splines

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arxiv 2110.04781 v1 pith:AXWV3RHR submitted 2021-10-10 math.NA cs.NA

V. Denysiuk This is my paper · ORCID
classification math.NAcs.NA
keywords splinespolynomialtrigonometricsimpleclassfourierseriestheory
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Classes of simple polynomial and simple trigonometric splines given by Fourier series are considered. It is shown that the class of simple trigonometric splines includes the class of simple polynomial splines. For some parameter values, the polynomial splines coincide with the trigonometric ones; this allows to transfer to such trigonometric splines all the results obtained for polynomial splines. Thus, it was possible to combine two powerful theories - the theory of trigonometric Fourier series and the theory of simple polynomial splines. The above material is illustrated by numerous examples.

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Cited by 1 Pith paper

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  1. Incomplete (even and odd) trigonometric splines in the problems of constructing approximate solutions of second order linear differential equations

    math.NA 2024-11 conditional novelty 4.0 of 10

    A collocation method based on incomplete even and odd trigonometric splines is developed for first boundary value problems of linear ODEs and illustrated on three examples.

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