In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial mapped bases allowing, for instance, to incorporate data or function discontinuities in a suitable mapping function. The new technique substantially mitigates the Runge's and Gibbs effects.
@article{arxiv.2204.01555,
title = {Polynomial mapped bases: theory and applications},
author = {Stefano De Marchi and Giacomo Elefante and Elisa Francomano and Francesco Marchetti},
journal= {arXiv preprint arXiv:2204.01555},
year = {2022}
}