aequationes mathematicae

, Volume 29, Issue 1, pp 183–203 | Cite as

Counterexamples in optimal quadrature

  • Arthur G. Werschulz
Research Papers


It is widely believed that order of exactness is a good measure of the quality of an algorithm for numerical quadrature. We show that this is not the case, by exhibiting a situation in which the optimal algorithm does not even integrate constants exactly. We also show that there are situations in which the penalty for using equidistant nodes is unbounded. Finally, we show that the complexity of obtaining an ɛ-approximation can be an arbitrary function of ɛ, i.e., there is no hardest quadrature problem.

AMS (1980) subject classification

Primary 65D30 Secondary 68C25 


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Copyright information

© Birkhäuser Verlag 1985

Authors and Affiliations

  • Arthur G. Werschulz
    • 1
    • 2
  1. 1.Division of Science and MathematicsFordham University/College at Lincoln CenterNew YorkUSA
  2. 2.Department of Computer ScienceColumbia UniversityNew YorkUSA

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