A review on the piecewise polynomial harmonic interpolation

Authors:
Sergio Amat Plata
Affiliations:
U.P. Cartagena, Applied Mathematics and Statistics, Alfonso 52, Cartagena, Murcia, Spain
Venue:
Applied Numerical Mathematics
Year:
2008

Citing 17
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Abstract

This paper surveys several topics related to a nonlinear centered piecewise polynomial interpolation technique. This interpolation leads to a nonlinear reconstruction operator with several desirable features: the reconstruction is fourth-order accurate in smooth regions, the data used is always centered with optimal support, the Gibbs phenomenon of linear reconstructions, in the presence of discontinuities, does not appear. Special attention is paid to the stability of the associated multiresolution transform. Finally, some applications are analyzed.