Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight
This paper deals with the construction of numerical methods for the estimation of integrals of the form \[ I(f) = {1\over(2\pi)^{n/2}} \int^\infty_{-\infty} \int^\infty_{-\infty} \cdots \int^\infty_{-\infty}e^{-x^Tx/2} f(x)dx_1,dx_2 \cdots dx_n \] with \(x=(x_1,x_2,\dots,x_n)^T\). Fully symmetric interpolatory integration rules are constructed for multidimensional integrals over infinite integration regions with a Gaussian weight function. The points for these rules are determined by successive extensions of the one-dimensional three-point Gauss-Hermite rule. The new rules are shown to be efficient and only moderately unstable.
fully symmetric interpolatory integration rules
scientific article; zbMATH DE number 910318