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(0, 1) Pál-type Interpolation: A General Method for Regularity

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Advanced Problems in Constructive Approximation

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 142))

Abstract

Hermite-Birkhoff interpolation and Pál-type interpolation have been receiving much attention over the years. Also during the previous 15 year the subject of interpolation in non-uniformly distributed nodes has been looked into.

The methods of proof of regularity often were quite dependent on the problem at hand, and the purpose of this note is to treat a possible ‘general’ method of finding polynomial pairs that lead to a regular interpolation problem; for sake of simplicity so-called (0, 1) Pál-type interpolation is looked into.

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References

  1. G.G. Lorentz, S.D. Riemenschneider and K. Jetter, Birkhoff Interpolation, Addison Wesley Pub. Co., Mass. USA, 1983.

    Google Scholar 

  2. Y. Bao, On simultaneous approximation to a differentiable function and its derivative by inverse Pál-type interpolation polynomials, Approx. Theory Appl. (N.S.) 11 (1995), 15–23.

    MathSciNet  MATH  Google Scholar 

  3. T.F. Xie and S.P. Zhou, On simultaneous approximation to a differentiable function and its derivative by Pál-type interpolation polynomials, Acta Math. Hungar. 69 (1995), 135–147.

    Article  MathSciNet  MATH  Google Scholar 

  4. Z.F. Sebestyén, Pál-type interpolation on the roots of Hermite polynomials, Pure math. Appl. 9 (1998), 429–439.

    MATH  Google Scholar 

  5. Marcel G. de Bruin, Interpolation on non-uniformly distributed nodes, Nonlinear Analysis 17 (2001), 1931–1940.

    Article  Google Scholar 

  6. Marcel G. de Bruin, Incomplete Pál-type interpolation, submitted.

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  7. Marcel G. de Bruin and Detlef H. Mache, (0, 2) Pál-type interpolation: A General Method for regularity, preprint.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematical Analysis, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    Marcel G. de Bruin

  2. Institute for Applied Mathematics (LS VIII), University of Dortmund, Vogelpothsweg 87, D-44221, Dortmund, Germany

    Detlef H. Mache

Authors
  1. Marcel G. de Bruin
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  2. Detlef H. Mache
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Editor information

Editors and Affiliations

  1. Mathematical Institute, Justus-Liebig University, Arndtstr. 2, D-35392, Giessen, Germany

    Martin D. Buhmann

  2. Institute of Applied Mathematics, University of Dortmund, Vogelpothsweg 87, D-44221, Dortmund, Germany

    Detlef H. Mache

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© 2002 Birkhäuser Verlag Basel

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de Bruin, M.G., Mache, D.H. (2002). (0, 1) Pál-type Interpolation: A General Method for Regularity. In: Buhmann, M.D., Mache, D.H. (eds) Advanced Problems in Constructive Approximation. ISNM International Series of Numerical Mathematics, vol 142. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7600-1_2

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  • DOI: https://doi.org/10.1007/978-3-0348-7600-1_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-7602-5

  • Online ISBN: 978-3-0348-7600-1

  • eBook Packages: Springer Book Archive

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