Extrapolation in distributed adaptive integration

Abstract

The paper addresses the design of distributed methods which incorporate numerical extrapolation into adaptive multivariate integration, in order to increase the functionality of the integration algorithms. When attempting to deal with singularities, adaptive integration algorithms need a very fine subdivision in the proximity of these "hot spots". This is not practical in higher dimensions where a vast number of subregions result. These problems may be alleviated through the use of a suitable extrapolation strategy. We present a strategy which, incorporated as a global extrapolation method in distributed adaptive integration, allows for load balancing.