BIT Numerical Mathematics

, Volume 40, Issue 1, pp 84–101

Adaptive Quadrature—Revisited

  • Walter Gander
  • Walter Gautschi

DOI: 10.1023/A:1022318402393

Cite this article as:
Gander, W. & Gautschi, W. BIT Numerical Mathematics (2000) 40: 84. doi:10.1023/A:1022318402393


First, the basic principles of adaptive quadrature are reviewed. Adaptive quadrature programs being recursive by nature, the choice of a good termination criterion is given particular attention. Two Matlab quadrature programs are presented. The first is an implementation of the well-known adaptive recursive Simpson rule; the second is new and is based on a four-point Gauss-Lobatto formula and two successive Kronrod extensions. Comparative test results are described and attention is drawn to serious deficiencies in the adaptive routines quad and quad8 provided by Matlab.

Adaptive quadrature Gauss quadrature Kronrod rules 

Copyright information

© Swets & Zeitlinger 2000

Authors and Affiliations

  • Walter Gander
    • 1
  • Walter Gautschi
    • 2
  1. 1.Institut für Wissenschaftliches RechnenETHZürichSwitzerland
  2. 2.Institut für Wissenschaftliches RechnenETHZürichSwitzerland

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