An Extension of Romberg Integration Procedures to N-Variables

The Romberg method of numerical integration is extended to multidimensional integration. The elements of the <italic>m</italic>th column of the Romberg array are shown to approximate up to <italic>0</italic>(<italic>h</italic><supscrpt>2<italic>m</italic>+2</supscrpt>) provided the integrand has 2<italic>m</italic>+2 bounded partial derivatives in each variable.