As well-known, a Gaussian quadrature formula Qnf is to be obtained by integration of a Hermitian interpolating polynomial Hn(f,x). Formulae Q̄nf of the same type can be obtained by integration of (math) where F(x) is an integral of f(x). It is characteristic for Qnf and Q̄nf, that the values f′(xi) and F(x.) respectively do not appear explicitly in Qn f and Q̄nf. Qnf and Q̄nf are said to be dual, if these are constructed in this way. The properties of these quadrature formulae are described here.


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  1. [1]
    Engels, H. Numerical Quadrature and Cubature, Academic Press 1980Google Scholar
  2. [2]
    Engels, H. Variation eines Themas von Gauß-Markoff, Vortrag bei der GAMM-Tagung 1981 in WürzburgGoogle Scholar
  3. [3]
    Merschen, A. Duale Quadraturen und ihre Eigenschaften (to appear)Google Scholar

Copyright information

© Springer Basel AG 1982

Authors and Affiliations

  • Hermann Engels
  • Anton Merschen

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