Rational quasi-Hermite-Fejér-type interpolation and Lobatto-type quadrature formula with Chebyshev-Markov nodes

• Yauheni Rouba ^[1] ; Kanstantin Smatrytski ^[1] ; Yauheni Dirvuk ^[1]
  1. [1] Yanka Kupala State University of Grodno

     Yanka Kupala State University of Grodno

     Bielorrusia

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 7, Nº. 2, 2015, págs. 291-308
• Idioma: inglés
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• Resumen

  • We present a quasi-Hermite-Fejér-type interpolation with nodes in the zeroes of Chebychev–Markov sine fractions. The convergence of the considered interpolation process for any continuous function on [−1, 1] is proved under the condition of the completeness of the corresponding system of rational functions. Next we construct Lobatto-type quadrature formula based on the quasi-Hermite-Fejér-type interpolation.

    We obtain coefficients of this quadrature in the explicit form. Also we derive convergence results for constructed quadrature formula.