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

Yauheni Rouba, Kanstantin Smatrytski, Yauheni Dirvuk

• 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.