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The error norm of Gaussian quadrature formulae for weight functions of Bernstein-Szegö type

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Summary

We consider the Gaussian quadrature formulae for the Bernstein-Szegö weight functions consisting of any one of the four Chebyshev weights divided by an arbitrary quadratic polynomial that remains positive on [−1, 1]. Using the method in Akrivis (1985), we compute the norm of the error functional of these quadrature formulae. The quality of the bounds for the error functional, that can be obtained in this way, is demonstrated by two numerical examples.

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References

  1. Akrivis, G.: Fehlerabschätzungen für Gauss-Quadraturformeln. Numer. Math.44, 261–278 (1984)

    Google Scholar 

  2. Akrivis, G., Burgstaller, A.: Fehlerabschätzungen für nichtsymmetrische Gauss-Quadraturformeln. Numer. Math.47, 535–543 (1985)

    Google Scholar 

  3. Akrivis, G.: The error norm of certain Gaussian quadrature formulae. Math. Comp.45, 513–519 (1985)

    Google Scholar 

  4. Gautschi, W., Notaris, S.E.: Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegö type. J. Comput. Appl. Math.25(2), 199–224 (1989); erratum in: J. Comput. Appl. Math.27 (3), 429 (1989)

    Google Scholar 

  5. Gautschi, W., Varga, R.S.: Error bounds for Gaussian quadrature of analytic functions. SIAM J. Numer. Anal.20, 1170–1186 (1983)

    Google Scholar 

  6. Gröbner, W., Hofreiter, N. (eds.) Integraltafel, II Teil. Wien: Springer 1961

    Google Scholar 

  7. Hämmerlin, G.: Fehlerabschätzungen bei numerischer Integration nach Gauss. In: Brosowski, B., Martensen, E. (eds.) Methoden und Verfahren der mathematischen Physik vol. 6, pp. 153–163. Mannheim, Wien, Zürich: Bibliographisches Institut 1972

    Google Scholar 

  8. Rivlin, T.J.: The Chebyshev Polynormials. New York: Wiley, 1974

    Google Scholar 

  9. Szegö, G.: Orthogonal Polynomials. Colloquium Publications, vol. 23, 4th ed., American Mathematical Society. Providence, RI, 1975

    Google Scholar 

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Notaris, S.E. The error norm of Gaussian quadrature formulae for weight functions of Bernstein-Szegö type. Numer. Math. 57, 271–283 (1990). https://doi.org/10.1007/BF01386411

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