A Divergent Sequence of Romberg Integrals.

Romberg integrals are built in order to accelerate the convergence of sequences of trapezoidal rules for approximating the definite integral of a continuous function f. While every sequence of trapezoidal rules with decreasing step length converges whenever f is continuous, this does not always hold for Romberg integrals. In this note we present a concrete example for which the sequence formed by the diagonal elements of the Romberg table diverges when the number of points used to compute the trapezoidal rules grows too slowly. [ABSTRACT FROM AUTHOR]