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.
De Marchi S., Elefante G., Francomano E., Marchetti F. (2022). Polynomial mapped bases: theory and applications. COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS, 13(1), 1-9 [10.2478/caim-2022-0001].
Polynomial mapped bases: theory and applications
Francomano E.;
2022-01-01
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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