Numerical integration of functions of very many variables

Haselgrove's method is currently considered to be the best for the numerical integration of smooth functions in very many (say, 6 or more) dimensions. This method, however, does not warrant the practically required accuracy of 3 significant decimals for integrands of remarkable variability. The method proposed in this paper introduces a skillful use of samplings to a multidimensional interpolatory quadrature scheme, and is shown to guarantee the above practical accuracy even where Haselgrove's method fails. This method has been devised especially for multivariable composite functions made up of complicated element functions of fewer variables.