Numerische Mathematik

, Volume 57, Issue 1, pp 123–138

Characterization of the speed of convergence of the trapezoidal rule

  • Qazi I. Rahman
  • Gerhard Schmeisser

DOI: 10.1007/BF01386402

Cite this article as:
Rahman, Q.I. & Schmeisser, G. Numer. Math. (1990) 57: 123. doi:10.1007/BF01386402


Our aim is to determine the precise space of functions for which the trapezoidal rule converges with a prescribed rate as the number of nodes tends to infinity. Excluding or controlling odd functions in some way it is possible to establish a correspondence between the speed of convergence and regularity properties of the function to be integrated. In this way we characterize Sobolev spaces, certain spaces of infinitely differentiable functions, of functions holomorphic in a strip, of entire functions of order greater than 1 and of entire functions of exponential type by the speed of convergence.

Subject Classifications

AMS(MOS): 41A55, 65D30, 46E10CR: G1.4

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Qazi I. Rahman
    • 1
  • Gerhard Schmeisser
    • 2
  1. 1.Départment de mathématiques et de statistiqueUniversité de MontréalMontréalCanada
  2. 2.Mathematisches InstitutUniversität Erlangen-NürnbergErlangenFederal Republic of Germany