Simultaneous Gaussian quadrature for Angelesco systems

• Doron S. Lubinsky ^[1] ; Walter Van Assche ^[2]
  1. [1] Georgia Institute of Technology

     Georgia Institute of Technology

     Estados Unidos

     
  2. [2] KU Leuven

     KU Leuven

     Arrondissement Leuven, Bélgica

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 8, Nº. 2, 2016, págs. 113-149
• Idioma: inglés
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• Resumen

  • We investigate simultaneous Gaussian quadrature for two integrals of the same function f but on two disjoint intervals. The quadrature nodes are zeros of a type II multiple orthogonal polynomial for an Angelesco system. We recall some known results for the quadrature nodes and the quadrature weights and prove some new results about the convergence of the quadrature formulas. Furthermore we give some estimates of the quadrature weights. Our results are based on a vector equilibrium problem in potential theory and weighted polynomial approximation.