A periodic map for linear barycentric rational trigonometric interpolation
- Berrut, Jean-Paul Department of Mathematics, University of Fribourg, Pérolles, Fribourg 1700, Switzerland
- Elefante, Giacomo Department of Mathematics, University of Fribourg, Pérolles, Fribourg 1700, Switzerland
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15.04.2020
Published in:
- Applied Mathematics and Computation. - 2020, vol. 371, p. 124924
English
Consider the set of equidistant nodes in [0, 2π),θk:=k·2πn,k=0,⋯,n−1.For an arbitrary 2π–periodic function f(θ), the barycentric formula for the corresponding trigonometric interpolant between the θk’s isT[f](θ)=∑k=0n−1(−1)kcst(θ−θk2)f(θk)∑k=0n−1(−1)kcst(θ−θk2),where cst(·):=ctg(·) if the number of nodes n is even, and cst(·):=csc(·) if n is odd. Baltensperger [3] has shown that the corresponding barycentric rational trigonometric interpolant given by the right-hand side of the above equation for arbitrary nodes introduced in [9] converges exponentially toward f when the nodes are the images of the θk’s under a periodic conformal map. In the present work, we introduce a simple periodic conformal map which accumulates nodes in the neighborhood of an arbitrarily located front, as well as its extension to several fronts. Despite its simplicity, this map allows for a very accurate approximation of smooth periodic functions with steep gradients.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 328446
- DOI 10.1016/j.amc.2019.124924
- Persistent URL
- https://folia.unifr.ch/unifr/documents/308513
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