A Review of Error Estimation in Adaptive Quadrature

The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated, and discussed. This article presents a review of existing error estimation techniques and discusses their differences and their common features. Some common shortcomings of these algorithms are discussed, and a new general error estimation technique is presented.