Rate of convergence of Shepard's global interpolation formula
Mathematics of Computation
Algorithm 792: accuracy test of ACM algorithms for interpolation of scattered data in the plane
ACM Transactions on Mathematical Software (TOMS)
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Error estimates for modified local Shepard's interpolation formula
Applied Numerical Mathematics
Lidstone approximation on the triangle
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Piecewise complementary Lidstone interpolation and error inequalities
Journal of Computational and Applied Mathematics
On the bivariate Shepard-Lidstone operators
Journal of Computational and Applied Mathematics
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Recently we have introduced a new technique for combining classical bivariate Shepard operators with three point polynomial interpolation operators (Dell'Accio and Di Tommaso, On the extension of the Shepard-Bernoulli operators to higher dimensions, unpublished). This technique is based on the association, to each sample point, of a triangle with a vertex in it and other ones in its neighborhood to minimize the error of the three point interpolation polynomial. The combination inherits both degree of exactness and interpolation conditions of the interpolation polynomial at each sample point, so that in Caira et al. (J Comput Appl Math 236:1691---1707, 2012) we generalized the notion of Lidstone Interpolation (LI) to scattered data sets by combining Shepard operators with the three point Lidstone interpolation polynomial (Costabile and Dell'Accio, Appl Numer Math 52:339---361, 2005). Complementary Lidstone Interpolation (CLI), which naturally complements Lidstone interpolation, was recently introduced by Costabile et al. (J Comput Appl Math 176:77---90, 2005) and drawn on by Agarwal et al. (2009) and Agarwal and Wong (J Comput Appl Math 234:2543---2561, 2010). In this paper we generalize the notion of CLI to bivariate scattered data sets. Numerical results are provided.