Adaptive quadrature - Revisited

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 rst 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.