Product type multiple integration formulas

Abstract

An integration formula of the type

$$\int_a^b {f(x)g(x)dx \cong \sum\limits_{i = 1}^N {\sum\limits_{j = 1}^M {a_{ij} f(xi)g(y_j ),} } } $$

referred to as a product quadrature, was first considered by R. Boland and C. Duris. In this paper, the author extends the concept of a product formula to multiple integrals. The definitions and some of the results for interpolatory, compound, and symmetric product quadratures have an analog for product cubatures and these are given.