A comparison of strategies for the automatic computation of two-dimensional integrals over infinite domains

We present sets of parameterized integral test families over each of the domains [0,infinity)(2) and (-infinity,infinity) 2, exhibiting various rates of integrand decay, and use these families to compare the performances of the two general-purpose two-dimensional cubature algorithms r2d2lri and Cubpack++ for integration over such nonfinite domains. The data collected for this comparison is helpful in identifying the respective advantages and disadvantages of the strategies adopted by the two algorithms when dealing with nonfinite domains.