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Complementary Lidstone interpolation on scattered data sets

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Abstract

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operators (Dell’Accio and Di Tommaso, On the extension of the Shepard-Bernoulli operators to higher dimensions, unpublished).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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università della Calabria, via P. Bucci 30A, 87036, Rende (Cs), Italy

    F. A. Costabile, F. Dell’Accio & F. Di Tommaso

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  1. F. A. Costabile
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  2. F. Dell’Accio
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  3. F. Di Tommaso
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Correspondence to F. Dell’Accio.

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Dedicated to Claude Brezinski and Sebastiano Seatzu on the occasion of their 70th birthday.

This paper is co-financed by the European Commission, European Social Fund and the Region of Calabria. The authors are solely responsible for this paper and the European Commission and the Region of Calabria are not responsible for any use that may be made of the information contained therein.

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Costabile, F., Dell’Accio, F. & Di Tommaso, F. Complementary Lidstone interpolation on scattered data sets. Numer Algor 64, 157–180 (2013). https://doi.org/10.1007/s11075-012-9659-6

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