Practical error estimation in adaptive multidimensional quadrature routines

摘要

In this paper we discuss various ways of improving the reliability of adaptive multidimensional quadrature routines. We discuss the reasons that estimates of the error over a given region of integration may fail in representing an upper bound for the actual error. On basis of this discussion we suggest different actions to be taken in order to improve the reliability of the quadrature routine. In the numerical experiments we study how these new error estimates work in practice.