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Asymptotics for Stieltjes polynomials, padé-type approximants, and Gauss-Kronrod quadrature

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Abstract

We study the asymptotic properties of Stieltjes polynomials outside the support of the measure as well as the asymptotic behaviour of their zeros. These properties are used to estimate the rate of convergence of sequences of rational functions, whose poles are partially fixed, which approximate Markovtype functions. An estimate for the speed of convergence of the Gauss-Kronrod quadrature formula in the case of analytic functions is also given.

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Authors and Affiliations

  1. Dpto. de Matemáticas Y Computación, Universidad de la Rioja, Edificio J. L. Vives Luis de Ulloa s/n, 26004, Logroño, Spain

    M. Bello Hernández

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

    B. de la Calle Ysern

  3. Dpto. de Matemáticas y Comptación, Universidad de la Rioja, Edificio J. L. Vives Luis de Ulloa s/n, 26004, Logroño, Spain

    J. J. Guadalupe Hernández

  4. Dpto. de Matemáticas Escuela Politécnica Superior, Universidad Carlos III de Madrid, Universidad 30, 28911, Leganés, Spain

    G. Lopez Lagomasino

Authors
  1. M. Bello Hernández
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  2. B. de la Calle Ysern
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  3. J. J. Guadalupe Hernández
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  4. G. Lopez Lagomasino
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Corresponding author

Correspondence to M. Bello Hernández.

Additional information

The work of M. Bello and J. J. Guadalupe was partially supported by DGES under grant PB96-0120-C03-02 and UR, AP-98/B12. J. J. Guadalupe died in a road accident on April 1, 2000. We, the co-authors, will miss a great friend, and the Spanish mathematical community his leadership and dedication to research. The work of G. López was partially supported by Dirección General de Enseñanza Superior under grant PB 96-0120-C03-01 and by INTAS under grant 93-0219 EXT.

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Bello Hernández, M., de la Calle Ysern, B., Guadalupe Hernández, J.J. et al. Asymptotics for Stieltjes polynomials, padé-type approximants, and Gauss-Kronrod quadrature. J. Anal. Math. 86, 1–23 (2002). https://doi.org/10.1007/BF02786642

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  • DOI: https://doi.org/10.1007/BF02786642

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