Independent sets of interpolation nodes or "how to make all sets regular"

Authors

  • Marcel G. de Bruin Delft University of Technology, Netherlands
  • Detlef H. Mache University of Applied Sciences Bochum, Technical University of Dortmund, Germany

DOI:

https://doi.org/10.33993/jnaat411-967

Keywords:

Pál-type interpolation, regularity
Abstract views: 224

Abstract

Hermite-Birkhoff interpolation and Pál-type interpolation have been receiving much attention over the years. Also during the previous 15 years the subject of interpolation in non-uniformly distributed nodes has been looked into. There are, however, not many examples known where lacunary problems (the orders of the derivatives for which data are given, are non-consecutive) are regular. Here lacunary Pál-type interpolation is looked into "the other way around": the interpolation points are given and the orders of the derivatives to be used are derived from the number of points.

 

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References

M.G. de Bruin and A. Sharma, Lacunary Pál-type interpolation and over-convergence, Comput. Methods Funct. Theory, 3, nos. 1-2, pp. 305-323, 2003. https://doi.org/10.1007/bf03321040 DOI: https://doi.org/10.1007/BF03321040

M.G. deBruin and D.H. Mache, Pál-type interpolation: a general method for regularity, Buhmann, M.D. & Mache, D.H. (ed.), Advanced problems in constructive approximation. 3rd IDoMAT, Witten-Bommerholz, Germany, August 20-24, 2001, Basel: Birkhäuser. ISNM, International Series of Numerical Mathematics, 142, pp. 21-26, 2003. https://doi.org/10.1007/978-3-0348-7600-1_2 DOI: https://doi.org/10.1007/978-3-0348-7600-1_2

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L.G. Pál, A new modification of the Hermite-Fejér interpolation, Anal. Math., 1, pp. 197-205, 1975. https://doi.org/10.1007/bf01930965 DOI: https://doi.org/10.1007/BF01930965

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Published

2012-01-01

How to Cite

de Bruin, M. G., & Mache, D. H. (2012). Independent sets of interpolation nodes or "how to make all sets regular". Rev. Anal. Numér. Théor. Approx., 41(1), 42–47. https://doi.org/10.33993/jnaat411-967

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