On a nonlinear interpolation procedure and its associated multiresolution scheme
نویسنده
چکیده
This paper surveys several topics related to a nonlinear centered piecewise polynomial interpolation technique and the associated multiresolution schemes. 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.
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