Chebyshev quadrature

  • Jaap Korevaar
Part of the Contemporary Mathematicians book series (CM)


Here we review Gautschi’s work on Chebyshev quadrature, first his 1975 survey paper, and then original work by him and his colaborators.


  1. 1.
    Andriy Bondarenko, Danylo Radchenko and Maryna Viazovska. Optimal asymptotic bounds for spherical designs. Ann. of Math. 178(2):443–452, 2013.Google Scholar
  2. 2.
    D. M. Kane. Small designs for path connected spaces and path connected homogeneous spaces. arXiv:1112.4900v2 [math.CO] 7 Apr 2012.Google Scholar
  3. 3.
    J. Korevaar and J. L. H. Meyers. Massive coalescence of nodes in optimal Chebyshevtype quadrature on [1, 1]. Indag. Math. (N. S.), 4(3):327–338, 1993.Google Scholar
  4. 4.
    J. Korevaar and J. L. H. Meyers. Spherical Faraday cage for the case of equal point charges and Chebyshev-type quadrature on the sphere. Integral Transform. Spec. Funct., 1(2):105–117, 1993.MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    J. Korevaar and J. L. H. Meyers. Chebyshev-type quadrature on multidimensional domains. J. Approx. Theory, 79(1):144–164, 1994.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Jacob Korevaar. Chebyshev-type quadratures: use of complex analysis and potential theory. Notes by Arno B. J. Kuijlaars. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 439, Complex potential theory (Montreal, PQ, 1993), 325–364, Kluwer Acad. Publ., Dordrecht, 1994.Google Scholar
  7. 7.
    J. Korevaar and L. Bos. Characterization of algebraic curves by Chebyshev quadrature. J. Anal. Math., 75(1):233–246, 1998.MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    J. Korevaar. Chebyshev quadrature recognizes algebraic curves and surfaces. In Approximation theory IX, Vol. I. (Nashville, TN, 1998), 165–174, Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, TN, 1998.Google Scholar
  9. 9.
    Arno Kuijlaars. The minimal number of nodes in Chebyshev type quadrature formulas. Indag. Math. (N. S.), 4(3):339–362, 1993.Google Scholar
  10. 10.
    J. L. H. Meyers. Chebyshev type quadrature formulas and potential theory. Ph.D. thesis, Univ. of Amsterdam, 1992 (79 pp).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Jaap Korevaar
    • 1
  1. 1.Korteveg de Vries InstitutUniversity of AmsterdamAmsterdamNetherlands

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