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The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type

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  • Orive, Ramón
  • Pejčev, Aleksandar V.
  • Spalević, Miodrag M.

Abstract

In this paper, we consider the Gauss quadrature formulae corresponding to some modifications of each of the four Chebyshev weights, considered by Gautschi and Li in [4]. As it is well known, in the case of analytic integrands the error of these quadrature formulas can be represented as a contour integral with a complex kernel. We study the kernel of the mentioned quadrature formulas on suitable elliptic contours, in such a way that the behavior of its modulus is analyzed in a rather simple manner, allowing us to derive some effective error bounds. In addition, some numerical examples checking the accuracy of such error bounds are included.

Suggested Citation

  • Orive, Ramón & Pejčev, Aleksandar V. & Spalević, Miodrag M., 2020. "The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319307982
    DOI: 10.1016/j.amc.2019.124806
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