Romberg extrapolation for Euler summation-based cubature on regular regions.

Abstract

Romberg extrapolation is a long-known method to improve the convergence rate of the trapezoidal rule on intervals. For simple regions such as the cube [Formula: see text] it is directly transferable to cubature in q dimensions. In this paper, we formulate Romberg extrapolation for Euler summation-based cubature on arbitrary q-dimensional regular regions [Formula: see text] and derive an explicit representation for the remainder term.