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Convergence Acceleration of Gauss–Chebyshev Quadrature Formulae

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Abstract

The aim of this paper is to accelerate, via extrapolation methods, the convergence of the sequences generated by the Gauss–Chebyshev quadrature formula applied to functions holomorphic in ]−1,1[ and possessing, in the neighborhood of 1 or −1, an asymptotic expansion with log (1±x)(1±x)α, (1±x)α, α>−1, as elementary elements.

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References

  1. C. Brezinski and M. Redivo-Zaglia, Extrapolation Methods. Theory and Practice (North-Holland, Amsterdam, 1991).

    Google Scholar 

  2. P.J. Davis and P. Rabinowitz, Methods of Numerical Integration (Academic Press, New York, 1984).

    Google Scholar 

  3. J. Dieudonné, Calcul Infinitésimal (Herman, Paris, 1968).

    Google Scholar 

  4. J.D. Donaldson and D. Elliott, A unified approach to quadrature rules with asymptotic estimates of their remainders, SIAM J. Numer. Anal. 9 (1972) 573–602.

    Google Scholar 

  5. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products (Academic Press, New York, 1992).

    Google Scholar 

  6. M. Kzaz, Gaussian quadrature and acceleration of convergence, Numer. Algorithms 15 (1997) 75–89.

    Google Scholar 

  7. P. Verlinden, Acceleration of Gauss–Legendre quadrature for an integrand with an endpoint singularity, J. Comput. Appl. Math. 77 (1997) 277–287.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Faculty of Sciences and Technique, B.P. 549, Marrakesh, Morocco

    M. Kzaz

  2. Laboratoire de Mathématiques Pures et Appliquées, Université du Littoral Côte d'Opale, Centre Universitaire de la Mi-Voix, 50 rue Ferdinand Buisson, B.P. 699, 62228, Calais Cédex, France

    M. Prévost

Authors
  1. M. Kzaz
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  2. M. Prévost
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Kzaz, M., Prévost, M. Convergence Acceleration of Gauss–Chebyshev Quadrature Formulae. Numerical Algorithms 34, 379–391 (2003). https://doi.org/10.1023/B:NUMA.0000005352.81665.7c

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  • DOI: https://doi.org/10.1023/B:NUMA.0000005352.81665.7c

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