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Adaptive Quadrature—Revisited

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Abstract

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.

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Authors and Affiliations

  1. Institut für Wissenschaftliches Rechnen, ETH, CH-8092, Zürich, Switzerland

    Walter Gander

  2. Institut für Wissenschaftliches Rechnen, ETH, CH-8092, Zürich, Switzerland

    Walter Gautschi

Authors
  1. Walter Gander
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  2. Walter Gautschi
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Gander, W., Gautschi, W. Adaptive Quadrature—Revisited. BIT Numerical Mathematics 40, 84–101 (2000). https://doi.org/10.1023/A:1022318402393

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