How well does the Hermite-Padé approximation smooth the Gibbs phenomenon?

@article{Beckermann2011HowWD,
title={How well does the Hermite-Pad{\'e} approximation smooth the Gibbs phenomenon?},
author={Bernhard Beckermann and Valeriy A. Kalyagin and Ana Cristina C Matos and Franck Wielonsky},
journal={Math. Comput.},
year={2011},
volume={80},
pages={931-958}
}

In order to reduce the Gibbs phenomenon exhibited by the partial Fourier sums of a periodic function f , defined on [−π, π], discontinuous at 0, Driscoll and Fornberg considered so-called singular Fourier-Padé approximants constructed from the Hermite-Padé approximants of the system of functions (1, g1(z), g2(z)), where g1(z) = log(1−z) and g2(z) is analytic, such that Re(g2(e)) = f(t). Convincing numerical experiments have been obtained by these authors, but no error estimates have been proven… CONTINUE READING