Automatic quadrature of functions of the formg(¦f(x¦)

Abstract

The standard routine QAGE from Quadpack is modified to allow the efficient evaluation of integrals of the form ∫ a b g(¦f(x)¦)dx, wheref andg are assumed to be smooth. Using function values available during the adaptive integration process, zeros off are found and used as subdivision points. The technique compares favourably with both the original bisection strategy and the nonuniform trisection strategy of Berntsen et al. The modified algorithm extends the class of integrals that can be integrated with an automatic code, since it copes with problem integrals that can not be integrated using the bisection or trisection strategies.