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Using Quasi-Interpolants in a Result of Favard

  • Thomas Kunkle
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 119)

Abstract

A proof of Favard can be restructured using quasi-interpolants of the type discussed in these proceedings [6] and his result strengthened.

Keywords

Weight Function Extension Theorem Smoothing Function Divided Difference Multivariate Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    de Boor C. A smooth and local interpolant with “small” kth derivative. In Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations, pages 177–197. Academic Press, New York, 1974. A. K. Aziz, ed.Google Scholar
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    de Boor C. How small can one make the derivatives of an interpolating function? J. Approx. Theory, 13: 105–116, 1975.MATHCrossRefGoogle Scholar
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    de Boor C. On “best” interpolation. J. Approx. Theory, 16: 28–42, 1976.MATHCrossRefGoogle Scholar
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    Favard J. Sur l’interpolation. J. Math. Pures Appl., 19: 281–300, 1940.MathSciNetMATHGoogle Scholar
  5. [5]
    Kunkle T. Lagrange interpolation on a lattice: bounding derivatives by divided differences. J. Approx. Theory, 71: 94–103, 1992.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Lei J., Cheney E. W. Quasi-interpolation on irregular points I. In these proceedings.Google Scholar

Copyright information

© Birkhäuser 1994

Authors and Affiliations

  • Thomas Kunkle
    • 1
  1. 1.Dept. of MathematicsCollege of CharlestonCharlestonUSA

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