Bounding the Lebesgue constant for a barycentric rational trigonometric interpolant at periodic well-spaced nodes

Berrut, Jean–Paul; Elefante, Giacomo

doi:10.1016/j.cam.2021.113664

Cited by 3 publications

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The latter fast convergence has been extended in [1] by Baltensperger to the interpolant (1) when the nodes are images of equidistant points under a periodic conformal map; an effective example of a periodic conformal map that clusters nodes around one (or more) location is presented and analysed in [4], this allows a faster convergence when the interpolated function present a front in one or more positions. The interpolant above, besides the fast convergence, present also a logarithmic growth of the Lebesgue constant for a wide class of nodes as proved in [5]. Another interesting barycentric rational trigonometric interpolant has been introduced in [2] and include Berrut's interpolant at equidistant nodes as a special case.…”

Section: Introductionmentioning

confidence: 99%

A barycentric trigonometric Hermite interpolant via an iterative approach

Elefante¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper an interative approach for constructing the Hermite interpolant introduced by Cirillo and Hormann (2018) for the Floater-Hormann family of interpolants is extended and generalised. In particular, we apply that scheme to produce an effective barycentric rational trigonometric Hermite interpolant using the basis function of the interpolant introduced by Berrut (1988). In order to give an easy construction of such an interpolant we compute the differentation matrix analytically and we conclude with various examples and a numerical study of the rate of convergence at equidistant nodes.

show abstract

Section: Introductionmentioning

confidence: 99%