A connection between Szegő–Lobatto and quasi Gauss-type quadrature formulas

• Ruymán Cruz-Barroso ^[1] ; Carlos Díaz Mendoza ^[1] ; Francisco Perdomo-Pío ^[1]
  1. [1] La Laguna University, Spain
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 284, Nº 1 (15 August 2015), 2015, págs. 133-143
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.11.021
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• Resumen

  • In this paper we obtain new results on positive quadrature formulas with prescribed nodes for the approximation of integrals with respect to a positive measure supported on the unit circle.

    We revise Szegő–Lobatto rules and we present a characterization of their existence. In particular, when the measure on the unit circle is symmetric, this characterization can be used to recover, in a more elementary way, a recent characterization result for the existence of positive quasi Gauss, quasi Radau and quasi Lobatto rules (quasi Gauss-type), due to B. Beckermann et. al. Some illustrative numerical examples are finally carried out in order to show the powerfulness of our results.