ABSTRACT

The earliest reference to numerical integration over three dimensional regions which I can find is 1877, in a paper familiarly referred to as "Maxwell's Brick". Since then the topic of numerical integration has been the subject of probably thousands of papers. Given a sufficiently smooth function f from R^s to R, the Cubature problem is to find numerical approximations to integrals over regions in s-dimensional space. This talk will describe a general class of methods to approximate such integrals. The methods are characterized by structure parameters which are chosen to satisfy certain constraints, while minimizing the number of function evaluations required. Some simple examples will be given.