A connection between Szego-Lobatto and quasi Gauss-type quadrature formulas

作者：Cruz Barroso Ruyman; Diaz Mendoza Carlos; Perdomo Pio Francisco^*

来源：Journal of Computational and Applied Mathematics, 2015, 284: 133-143.

DOI：10.1016/j.cam.2014.11.021

• Szego-Lobatto quadrature formulas
• Gauss, Radau and Lobatto quadrature formulas
• Prescribed nodes
• Szego polynomials
• Para-orthogonal polynomials

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 Szego-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.

• 出版日期2015-8-15