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On the Minimal Variance of Quadrature Formulas

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Numerical Integration III

Abstract

If function values have random error, it is of practical interest that the quadrature formulas Qn being used have small variance Var(Qn). The purpose of this paper is to investigate upper and lower bounds for

$$\mathop {\deg \left( {{Q_n}} \right)}\limits^{\inf } \geqslant m\quad Var\left( {{Q_n}} \right)$$

, where deg(Qn) denotes the algebraic degree of Qn.

AMS (1980) Subject Classification: 65.D.30

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Technischen Universität Braunschweig, Pockelsstr. 14, D - 3300, Braunschweig, Germany

    Privatdozent Dr. rer. nat. habil. Klaus-Jürgen Förster

Authors
  1. Privatdozent Dr. rer. nat. habil. Klaus-Jürgen Förster
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Editors and Affiliations

  1. Institut für angewandte Mathematik, TU Braunschweig, Pockelsstrasse 14, D-3300, Braunschweig, Germany

    H. Braß

  2. Mathematisches Institut, Ludwig-Maximilian-Universität, Theresienstrasse 39, D-8000, München 2, Germany

    G. Hämmerlin

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Förster, KJ. (1988). On the Minimal Variance of Quadrature Formulas. In: Braß, H., Hämmerlin, G. (eds) Numerical Integration III. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 85. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6398-8_4

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  • DOI: https://doi.org/10.1007/978-3-0348-6398-8_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-2205-2

  • Online ISBN: 978-3-0348-6398-8

  • eBook Packages: Springer Book Archive

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