Advertisement

Israel Journal of Mathematics

, Volume 16, Issue 3, pp 287–299 | Cite as

Numerical integration rules near gaussian quadrature

  • C. A. Micchelli
  • T. J. Rivlin
Article

Abstract

We call a numerical integration formula based onk nodes which is exact for polynomials of degree at mostn an (n, k) formula. Gaussian quadrature is the unique (2k−1,k) formula. In this paper we give a complete description of all (2k−3,k) formulas, including a characterization of those having all positive weights.

Keywords

Orthogonal Polynomial Quadrature Formula Gaussian Quadrature Cusp Point YORKTOWN Height 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Fejér,Mechanische Quadraturen mit positiven Cotesschen Zahlen, Math. Z.37 (1933), 287–309.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    L. Fejér,Gesammelte Arbeiten, 2 vols., Birkhauser, Basel, 1970.MATHGoogle Scholar
  3. 3.
    J. L. Soulé,Formules de quadrature contrôlée, Rapport No. 23, Dep't. de Calcul Electronique, Comm. à L'Energie Atomique, 1966.Google Scholar
  4. 4.
    G. Szegö,Orthogonal polynomials, Amer. Math. Soc., New York, 1959.MATHGoogle Scholar

Copyright information

© Hebrew University 1973

Authors and Affiliations

  • C. A. Micchelli
    • 1
  • T. J. Rivlin
    • 1
  1. 1.IBM Research CenterYorktown HeightsU.S.A.

Personalised recommendations