A quantum mechanical test of diophantine methods

A blend of Haselgrove's method and the biased selection method for evaluating multidimensional integrals was tested. The results were mixed. The error estimate varied from being proportional to 1/N when N was less than ca. 60,000 to being proportional to 1/√N when N was greater than 60,000. Also, for N greater than 60,000, the error estimate was one-half the error estimate given by biased selection alone. These numbers should be compared with the 10,000 points used to find an optimum set of Haselgrove's parameters. It is reasonable to expect that if 100,000 points were used in the optimization of Haselgrove's parameters that the above results would be found with 60,000 replaced by 600,000.