On iterated numerical integration

Abstract

We revisit the iterated numerical integration method and show that it is extremely efficient in solving certain classes of problems. A multidimensional integral can be approximated by a combination of lower-dimensional or one-dimensional adaptive methods iteratively. When an integrand contains sharp ridges which are not parallel with any axis, iterated methods often outperform adaptive cubature methods in low dimensions. We use examples to support our analysis. © Springer-Verlag Berlin Heidelberg 2005.