Positive rational interpolatory quadrature formulas on the unit circle and the interval

• Autores: Karl Deckers, Adhemar Bultheel , Ruymán Cruz Barroso, Francisco José Perdomo Pío
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 60, Nº. 12, 2010, págs. 1286-1299
• Idioma: inglés
• DOI: 10.1016/j.apnum.2010.03.018
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• Resumen

  • We present a relation between rational Gauss-type quadrature formulas that approximate integrals of the form View the MathML source, and rational Szego" quadrature formulas that approximate integrals of the form View the MathML source. The measures ? and View the MathML source are assumed to be positive bounded Borel measures on the interval [-1,1] and the complex unit circle respectively, and are related by View the MathML source. Next, making use of the so-called para-orthogonal rational functions, we obtain a one-parameter family of rational interpolatory quadrature formulas with positive weights for J?(F). Finally, we include some illustrative numerical examples.