On certain symmetric strong distributions, two-point Padé approximation and related quadratures

• Autores: Carlos Javier Díaz Mendoza, Pablo González Vera, Mateo Miguel Jiménez Paiz, Ramón Angel Orive Rodríguez
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 59, Nº. 8, 2009, págs. 2002-2014
• Idioma: inglés
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• Resumen

  • Let phi be a c-inversive strong distribution as defined in [A. Sri Ranga, E.X.L. de Andrade, J.H. McCabe, Some consequences of a symmetry in strong distributions, J. Math. Anal. Appl. 193 (1) (1995) 158�168]. In this paper, two-point Padé approximants, both with free and prescribed poles, related to the distribution phi are analyzed. In particular, the existence of c-inversive rational approximants to the Stieltjes transform of phi is studied, in order to make computations in an advantageous way. An application to numerical quadratures is also given, and several examples applying these Gauss-type quadrature formulas in the case of integrands which can be well approximated by Laurent polynomials are displayed, showing better results than the corresponding for the usual Gaussian rules.