On the bivariate Shepard-Lidstone operators

Authors:
R. Caira;F. Dell'Accio;F. Di Tommaso
Affiliations:
-;-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

Citing 6
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Abstract

We propose a new combination of the bivariate Shepard operators (Coman and Trimbitas, 2001 [2]) by the three point Lidstone polynomials introduced in Costabile and Dell'Accio (2005) [7]. The new combination inherits both degree of exactness and Lidstone interpolation conditions at each node, which characterize the interpolation polynomial. These new operators find application to the scattered data interpolation problem when supplementary second order derivative data are given (Kraaijpoel and van Leeuwen, 2010 [13]). Numerical comparison with other well known combinations is presented.