A connection between Szeg-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 Szeg-Lobatto rules and we present a characterization of their existence. In particular, when the mea...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 284; pp. 133 - 143
Main Authors Cruz-Barroso, Ruyman, Mendoza, Carlos Diaz, Perdomo-Pio, Francisco
Format Journal Article
LanguageEnglish
Published 01.08.2015
Subjects
Approximation
Computation
Integrals
Mathematical analysis
Mathematical models
Quadratures
Symmetry
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Summary: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 Szeg-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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ISSN:0377-0427
DOI:10.1016/j.cam.2014.11.021