Purpose of this document

This document shows where the CUHRE algorithm evaluates the function it is integrating. Unlike a Monte Carlo algorithm (such as VEGAS), CUHRE evaluates the function at a set of determinalistically chosen points.

The function used as the integrand in this example is:

\[ 2 x^2 + 2 y - y^2.\] We have used both VEGAS and CUHRE to integrate this function, using a fractional error tolerance of 0.01. This function is sufficiently simple that CUHRE uses only two regions. The plots show where VEGAS and CUHRE each evaluate the function to achieve this level of accuracty.

VEGAS required 2500 function evaluations, and CUHRE required 195.