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

Abstract

In this paper, we propose several approximations of a multivariate function by quasiinterpolants 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 C2 quintic spline quasi-interpolation. Finally, numerical tests are presented to show the approximation power of these quasi-interpolants. © 2012 Elsevier Ltd. All rights reserved.

DOI: 10.1016/j.camwa.2012.10.006

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Cite this paper

@article{Barrera2013ConstructionTF, title={Construction techniques for multivariate modified quasi-interpolants with high approximation order}, author={Domingo Barrera and Allal Guessab and Mar{\'i}a J. Ib{\'a}{\~n}ez and O. Nouisser}, journal={Computers & Mathematics with Applications}, year={2013}, volume={65}, pages={29-41} }