Ruymán Cruz Barroso, Carlos Javier Díaz Mendoza, Francisco José Perdomo Pío
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.
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