@misc{10481/93468,
year = {2024},
month = {6},
url = {https://hdl.handle.net/10481/93468},
abstract = {In this paper we propose the use of 𝐶������1-continuous cubic quasi-interpolation schemes expressed
in Bernstein–Bézier form to approximate functions with jumps. The construction of these
schemes is explicit and consists of directly attaching the Bernstein–Bézier coefficients to
appropriate combinations of the given data values. This construction can lead to quasiinterpolation
schemes with free parameters. This allows to write these schemes of optimal
convergence order as a non-negative convex combination of certain quasi-interpolation schemes
of lower convergence order. The idea behind that, is to divide the data set used to define a quasiinterpolant
of optimal order into subsets, and then define the associated quasi-interpolants.
The free parameters facilitate the choice of the convex combination weights. We then apply
the WENO approach to the weights to eliminate the Gibbs phenomenon that occurs when we
approximate in a non-smooth region. The proposed schemes are of optimal order in the smooth
regions and near optimal order is achieved in the neighboring region of discontinuity.},
organization = {Spanish MINECO project PID2020-117211GB-I00
and GVA project CIAICO/2021/227},
organization = {PAIDI programme of the Junta de Andalucía, Spain},
organization = {MUR Excellence Department Project awarded to the Department of Mathematics, University of
Rome Tor Vergata, CUP E83C23000330006},
publisher = {Elsevier},
keywords = {Bernstein–Bézier representation},
keywords = {Quasi-interpolation},
keywords = {WENO-ENO},
title = {ENO and WENO cubic quasi-interpolating splines in Bernstein–Bézier form},
doi = {10.1016/j.matcom.2024.06.001},
author = {Aràndiga, F. and Barrera Rosillo, Domingo and Eddargani, Salah},
}