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Rational quadrature formulae on the unit circle with arbitrary poles

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Abstract

Interpolatory quadrature rules exactly integrating rational functions on the unit circle are considered. The poles are prescribed under the only restriction of not lying on the unit circle. A computable upper bound of the error is obtained which is valid for any choice of poles, arbitrary weight functions and any degree of exactness provided that the integrand is analytic on a neighborhood of the unit circle. A number of numerical examples are given which show the advantages of using such rules as well as the sharpness of the error bound. Also, a comparison is made with other error bounds appearing in the literature.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, E.T.S. Ingenieros Industriales, Universidad Politécnica de Madrid, José G. Abascal 2, 28006, Madrid, Spain

    B. de la Calle Ysern

  2. Departamento de Análisis Matemático, Universidad de La Laguna, 38271, La Laguna, Tenerife, Spain

    P. González-Vera

Authors
  1. B. de la Calle Ysern
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  2. P. González-Vera
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Correspondence to B. de la Calle Ysern.

Additional information

The work of the first author was supported by the Dirección General de Investigación, Ministerio de Educación y Ciencia, under grants MTM2006-13000-C03-02 and MTM2006-07186 and by UPM and Comunidad de Madrid under grant CCG06-UPM/MTM-539. The work of the second author was partially supported by the Dirección General de Investigación, Ministerio de Educación y Ciencia, under grant MTM2005-08571.

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de la Calle Ysern, B., González-Vera, P. Rational quadrature formulae on the unit circle with arbitrary poles. Numer. Math. 107, 559–587 (2007). https://doi.org/10.1007/s00211-007-0102-1

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  • DOI: https://doi.org/10.1007/s00211-007-0102-1

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