Numerische Mathematik

, Volume 9, Issue 3, pp 200–213 | Cite as

Error bounds for the evaluation of integrals by repeated gauss-type formulae

  • Frank Stenger
Article

Keywords

Mathematical Method Error Bound 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Mises, R. von: Numerische Berechnung mehrdimensionaler Integrale. Z. Angew. Math. Mech.34, 201–210 (1954).Google Scholar
  2. [2]
    Sard, A.: New function spaces and their adjoints. Ann. N. Y. Acad. Sci.86, 700–757 (1960).Google Scholar
  3. [3]
    Davis, P. J.: Errors of numerical approximation for analytic functions, Survey of numerical analysis, ed. byJ. Todd. New York: McGraw-Hill Book Inc. 1962.Google Scholar
  4. [4]
    McNamee, J.: Error bounds for the evaluation of integrals by the Euler-Maclaurin formula and by Gauss-type formulae. Math. Comput.18, 368–381 (1964).Google Scholar
  5. [5]
    Hämmerlin, G.: Ableitungsfreie Schranken für Quadraturfehler. Num. Math.5, 226–233 (1963).CrossRefGoogle Scholar
  6. [6]
    Stehger, F.: Bounds on the error of Gauss-type quadratures. Num. Math.8, 150–160 (1966).CrossRefGoogle Scholar
  7. [7]
    Todd, J.: Survey of numerical analysis. New York: McGraw-Hill Book-Inc. 1962.Google Scholar
  8. [8]
    Meinardus, G.: Approximation von Funktionen und ihre Numerische Behandlung. Berlin-Göttingen-Heidelberg: Springer 1964.Google Scholar
  9. [9]
    National Bureau of Standards. Handbook of mathematical. functions. Applied Math. Series vol. 55. 1964.Google Scholar
  10. [10]
    McNamee, J., andF. Stehger: Construction of fully symmetric numerical integration formulas. To be published.Google Scholar
  11. [11]
    Nikol'skii, S. M.: Quadrature formulae [Russian]. Moscow: Fizmatgiz (Gos. Izdat. Fiz. Mat. Lit.) 1958. 1958.Google Scholar
  12. [12]
    Ahlin, A. C.: On error bounds for Gaussian cubature. SIAM Rev.4, 25–39 (1962).CrossRefGoogle Scholar
  13. [13]
    Stroud, A. H., andD. Secrest: Gaussian quadrature formulas. New York: Prentice-Hall 1966.Google Scholar

Copyright information

© Springer-Verlag 1966

Authors and Affiliations

  • Frank Stenger
    • 1
  1. 1.Department of MathematicsThe University of MichiganAnn ArborUSA

Personalised recommendations