A comparison of different progressive iteration approximation methods

Authors:
Jorge Delgado;Juan Manuel Peña
Affiliations:
Dept. Applied Mathematics, University of Zaragoza, Escuela Universitaria Politécnica de Teruel, Teruel, Spain;Dept. Applied Mathematics/IUMA, University of Zaragoza, Zaragoza, Spain
Venue:
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Year:
2008

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Abstract

The progressive iteration approximation property (PIA) permits applying tools of CAGD to the interpolation of curves and surfaces. Convergence rates of PIA for bases of different spaces are analyzed and compared, including tables of rate of convergence and figures. In the rational case, the importance of an adequate choice of the weights and of an adequate evaluation algorithm is shown. Finally, a new approach to the PIA is introduced.