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Global smoothness preservation by bivariate interpolation operators

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Analysis in Theory and Applications

Abstract

Extending the results of [4] in the univariate case, in this paper we prove that the bivariate interpolation polynomials of Hermite-Fejér based on the Chebyshev nodes of the first kind, those of Lagrange based on the Chebyshev nodes of second kind and ±1, and those of bivariate Shepard operators, have the property of partial preservation of global smoothness, with respect to various bivariate moduli of continuity.

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Authors and Affiliations

  1. Department of Mathematics, University of Oradea, Str. Armatei Komane 5, 3700, Oradea, Romania

    S. G. Gal

  2. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Science, P. O. Box 127, H-1364, Budapest, Haungary

    J. Szabados

Authors
  1. S. G. Gal
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  2. J. Szabados
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Gal, S.G., Szabados, J. Global smoothness preservation by bivariate interpolation operators. Anal. Theory Appl. 19, 193–208 (2003). https://doi.org/10.1007/BF02835279

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  • DOI: https://doi.org/10.1007/BF02835279

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