Treating the Gibbs phenomenon in barycentric rational interpolation and approximation via the S-Gibbs algorithm

摘要

In this work, we extend the so-called mapped bases or fake nodes approach to the barycentric rational interpolation of Floater-Hormann and to AAA approximants. More precisely, we focus on the reconstruction of discontinuous functions by the S-Gibbs algorithm introduced in De Marchi et al. (2020). Numerical tests show that it yields an accurate approximation of discontinuous functions. (C) 2019 Elsevier Ltd. All rights reserved.