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

Berrut, Jean-Paul; De Marchi, Stefano; Elefante, Giacomo; Marchetti, Francesco

doi:10.1016/j.aml.2019.106196

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Journal article

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

Berrut, Jean-Paul Département de Mathématiques, Université de Fribourg, Switzerland
De Marchi, Stefano Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, Italy
Elefante, Giacomo Département de Mathématiques, Université de Fribourg, Switzerland
Marchetti, Francesco Dipartimento di Salute della Donna e del Bambino, Università di Padova, Italy

01.05.2020

Published in:

Applied Mathematics Letters. - 2020, vol. 103, p. 106196

English 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.

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language