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Quadratic convergence of approximations by CCC-Schoenberg operators

Numerische Mathematik volume 135, pages 1253–1287 (2017)Cite this article

Abstract

We generalize to the Canonical Complete Chebyshev splines some properties already known for Extended Chebyshev and piecewise Extended Chebyshev splines, like Marsden identity and Greville points. Also, we represent an interesting algorithm which leads to numerically stable expressions for the Greville points for CCC-splines. We show that any CCC-spline space provides us with infinite number of operators of the Schoenberg-type, and we give a simple characterization of them. After proving few important properties, we establish a sufficient condition for quadratic convergence of approximations by CCC-Schoenberg operators to a given function.

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Acknowledgments

This research was supported by Ministry of science, education and sports of the Republic of Croatia under Grant 037-1193086-2771.

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Authors and Affiliations

  1. University of Zagreb, Faculty of Science, Department of Mathematics, Bijenička 30, Zagreb, Croatia

    Tina Bosner & Mladen Rogina

Authors
  1. Tina Bosner
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  2. Mladen Rogina
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Corresponding author

Correspondence to Tina Bosner.

Additional information

This article is in memory and honor of Mladen Rogina who passed away on 24 January 2013, as our last joint work.

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Bosner, T., Rogina, M. Quadratic convergence of approximations by CCC-Schoenberg operators. Numer. Math. 135, 1253–1287 (2017). https://doi.org/10.1007/s00211-016-0831-0

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  • DOI: https://doi.org/10.1007/s00211-016-0831-0

Mathematics Subject Classification

  • 41A15
  • 41A25
  • 41A35
  • 41A50
  • 65D07
  • 65D17