On an interpolatory method for high dimensional integration

We discuss numerical integration of smooth functions that are defined on a bounded or unbounded hyperrectangular region. We present numerical results that demonstrate the wide range of applications for our recently invented method. In addition, we survey theoretical results. In the fully symmetric case our method is a special fully symmetric rule. However, we also have error bounds (not available for general fully symmetric rules) and the method also can be used if the weight function is an arbitrary tensor product with different and/or nonsymmetric factors.