A periodic map for linear barycentric rational trigonometric interpolation

Jean-Paul Berrut and Giacomo Elefante

Applied Mathematics and Computation, 2020, vol. 371, issue C

Abstract: 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.

Keywords: Barycentric rational interpolation; Trigonometric interpolation; Conformal maps (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319309166
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:371:y:2020:i:c:s0096300319309166

DOI: 10.1016/j.amc.2019.124924

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().