Polynomial mapped bases: theory and applications

Stefano De Marchi; Giacomo Elefante; Elisa Francomano; Francesco Marchetti

doi:10.2478/caim-2022-0001

Abstract

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.

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Polynomial mapped bases: theory and applications

Abstract

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