Key points are not available for this paper at this time.
General properties of automatic quadrature routines are described, and the conflict between reliablhty and economy whmh arises when one constructs such a routine is discussed m detail. The concept of the "performance profile" is introduced; this serves as an aid m understanding how such routines may fail for some problems and why the cost IS so much higher than in a nonautomatic routine. The relationship (often tenuous) between analytic results from numerical analysis relating to quadrature rules and the actual strategy used in these routines is discussed. Attention is drawn to the fact that an automatm quadrature routine is based on an unrehable exact arithmetic algorithm and, unlike simpler routines, is not based on a finite decision process. In this paper, those aspects of automatm quadrature routines which are relevant in the context of testing routines are gathered together as an introduction to forthcoming specific testing techmques.
Lyness et al. (Mon,) studied this question.