Local Versus Global Strategies for Adaptive Quadrature

Abstract

A study has been made of two alternative subinterval selection strategies for adaptive quadrature. The more commonly used is termed a local acceptance criterion (as in SQUANK), and the other is termed a global acceptance criterion (as in AIND). An efficient programming technique for the global alternative is given, and an analytic model for predicting the subinterval distributions selected by classes of adaptive algorithms is developed. To test tile predictions of the model, the well-known algorithm SQUANK was reprogrammed to make it operate under the global criterion. Experiments with these routines were carried out comparing their actual performance with the predicted performance and with the performance of CADRE and AIND, and some conclusions are drawn. © 1975, ACM. All rights reserved.