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On Mean Convergence of Lagrange-Kronrod Interpolation

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

Abstract

It is known that Lagrange interpolation to any continuous function on [-1, 1] at the zeros of an orthogonal polynomial converges in the mean. In this paper we study mean convergence of Lagrange-Kronrod interpolation where the nodes are the n zeros of an orthogonal polynomial of degree n and the n + 1 zeros of the associated Stieltjes polynomial of degree n + 1. A sufficient condition for mean convergence, due to P. Erdös and P. Turán, is shown to hold for the first-, the third- and fourth-kind Chebyshev weight functions.

Keywords

Weight Function Orthogonal Polynomial Quadrature Formula Lagrange Interpolation Lagrange Interpolation Polynomial 
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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Copyright information

© Birkhäuser 1994

Authors and Affiliations

  • Shikang Li
    • 1
  1. 1.Department of MathematicsSoutheastern Louisiana UniversityHammondUSA

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