Korovkin-type convergence results for multivariate Shepard formulae

Authors

  • Oliver Nowak Technical University of Braunschweig, Germany

DOI:

https://doi.org/10.33993/jnaat382-912

Keywords:

Shepard formula, Shepard interpolation, multivariate scattered data interpolation, approximation by positive operators
Abstract views: 193

Abstract

We present a new convergence proof for classic multivariate Shepard formulae within the context of Korovkin-type convergence results for positive operators on spaces of continuous real valued functions.

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References

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Nowak, O., Korovkin-type convergence results for non-positive operators, in preparation.

Nowak, O. and Sonar, Th., Upwind-biased finite difference formulae from moving least squares interpolation, in preparation.

Shepard, D., A two-dimensional interpolation function for irregularly-spaced data, Proc. ACM National Conference, pp. 517-524, 1968. DOI: https://doi.org/10.1145/800186.810616

Sonar, Th., Difference operators from interpolating moving least squares and their deviation from optimality, ESAIM, M2AN, 39(5), pp. 883-908, 2005, https://doi.org/10.1051/m2an:2005039 DOI: https://doi.org/10.1051/m2an:2005039

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Published

2009-08-01

How to Cite

Nowak, O. (2009). Korovkin-type convergence results for multivariate Shepard formulae. Rev. Anal. Numér. Théor. Approx., 38(2), 170–176. https://doi.org/10.33993/jnaat382-912

Issue

Vol. 38 No. 2 (2009)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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