Construction techniques for multivariate modified quasi-interpolants with high approximation order

Authors:
D. Barrera;A. Guessab;M. J. IbáñEz;O. Nouisser
Affiliations:
Departamento de Matemática Aplicada, Universidad de Granada, 18071-Granada, Spain;Laboratoire de Mathématiques Appliquées (UMR CNRS 5142), Université de Pau et des Pays de l'Adour - BP 1155 64013 Pau Cedex, France;Departamento de Matemática Aplicada, Universidad de Granada, 18071-Granada, Spain;Département de Mathématiques et Informatique, Université Cadi-Ayyad, Faculté Polydisciplinaire de Safi, 46000-Safi, Maroc
Venue:
Computers & Mathematics with Applications
Year:
2013

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Abstract

In this paper, we propose several approximations of a multivariate function by quasi-interpolants on non-uniform data and we study their properties. In particular, we characterize those that preserve constants via the partition of unity approach. As one of the main results, we show how by a very simple modification of a given quasi-interpolant it is possible to construct new quasi-interpolants with remarkable properties. We also provide some results regarding bivariate C^2 quintic spline quasi-interpolation. Finally, numerical tests are presented to show the approximation power of these quasi-interpolants.