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

Berrut, Jean-Paul ; Marchi, S. De ; Elefante, Giacomo ; Marchetti, F.

In: Applied Mathematics Letters, 2020, vol. 103, p. 106196

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.