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Some Erdös-type Convergence Processes in Weighted Interpolation

  • László Szili
  • Péter Vértesi
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 142)

Abstract

In 1943, P. Erdös [5] showed that if the interpolation point system X n C [-1, 1] (n ∈ N) such that the fundamental polynomials of Lagrange interpolation are uniformly bounded in [-1, 1] then for every fC[-1, 1] and c > 0 there exists a sequence of polynomials ϕ n of degree ≤ n(l+c) (n ∈ N) which interpolates f at the points X n and it tends to f uniformly in [-1, 1]. The weighted versions of this result were proved in [19] and [18] using Freud-type weights and exponential weights on [-1, 1]. The aim of this paper is to show that analogue statements are true for weighted interpolation if we consider Erdös-type and some ultraspherical weights.

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Copyright information

© Birkhäuser Verlag Basel 2002

Authors and Affiliations

  • László Szili
    • 1
  • Péter Vértesi
    • 2
  1. 1.Department of Numerical AnalysisLoránd Eötvös UniversityBudapestHungary
  2. 2.Rényi Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary

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