Integration over multidimensional hypercubes I. A

J. N. Lyness and B. J. J. McHugh A method of numerical integration is described which uses a low order integration rule to obtain a high order result The error is successively reduced, using a method based on the idea of Richardson's deferred approach to the limit. The method is restricted to hypercubic domains. The standard methods of multidimensional numerical integration require the evaluation of the function at a number of points. The effort spent is normally directly proportional to the number of such evaluations, and consequently it is desirable to obtain an accurate result with as few function evaluations as possible. Methods based on random procedures, such as the Monte Carlo method (Davis and Rabinowitz, 1956), and the recent method using Cesaro Sums (Haselgrove, 1961,) are easy to code and, as the number of points is increased, convergence of successive results may be observe