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

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.