When Not to Use an Automatic Quadrature Routine
James N. Lyness · SIAM Review · 1983
Numerical quadrature is required as a component in many large scale (and small scale) scientific programs. Frequently the scientist faces a choice. Either he may use one of the comparatively recent automatic quadrature routines (AQR) or he may use a standard rule evaluation quadrature routine (REAR) based directly on traditional formulae. The purpose of this article is to help the scientist to make an informed choice. In the first half of this article we introduce some generic properties of AQRs. The more straightforward of these are those concerned with reliability and economy. Less straightforward is the vital “performance profile” property. The second half of this article is devoted principally to demonstrating how in some calculations the jagged performance profile associated with the AQR can cause other parts of the overall program to be far more expensive than necessary. Thus, while in many programs, the use of an AQR can save significant human time, in many other programs, its use can be a disaster. There is no information in this article about particular AQRs or REQRs. This article is concerned only with generic properties of these two fundamentally different categories of numerical software.