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Fehlerabschätzungen für nichtsymmetrische Gauß-Quadraturformeln

Error estimates for nonsymmetric Gaussian quadrature formulae

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Summary

We consider Gaussian quadrature formulaeQ n , n∈ℕ, approximating the integral\(I(f): = \int\limits_{ - 1}^1 {w(x)f(x)dx} \), wherew is a weight function. In certain spaces of analytic functions the error functionalR n :=I−Q n is continuous. Previously one of the authors deduced estimates for ‖R n ‖ for symmetric Gaussian quadrature formulae. In this paper we extend these results to nonsymmetric Gaussian formulae using a recent result of Gautschi concerning the sign ofR n (q K ),q K (x):=x K, for a wide class of weight functions including the Jacobi weights.

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Author notes

  1. G. Akrivis

    Present address: Department of Mathematics, University of Crete, P.O. Box 470, Iraklion Crete, Greece

Authors and Affiliations

  1. Mathematisches Institut der Ludwig-Maximilians-Universität, Theresienstr. 39, D-8000, München 2, Bundesrepublik Deutschland

    G. Akrivis & A. Burgstaller

Authors
  1. G. Akrivis
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  2. A. Burgstaller
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Akrivis, G., Burgstaller, A. Fehlerabschätzungen für nichtsymmetrische Gauß-Quadraturformeln. Numer. Math. 47, 535–543 (1985). https://doi.org/10.1007/BF01389455

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