An implementation of verified Gaussian quadrature involves algorithmic parameters whose correct setting is crucial for adequate performance. We identify several of these control parameters and, based on experimental data, we try to give advice for choosing suitable parameter values in order to obtain reasonable average performance for a “black-box” quadrature routine.

This paper compares several strategies for subdividing the domain in verified multi-dimensional Gaussian quadrature. Subdivision may be used in two places in the quadrature algorithm. First, subdividing the box can reduce the over-estimation of the partial derivatives' ranges, which are needed to bound the approximation error. Second, if the required error bound cannot be met with the whole domain then the box is split into subboxes, and the quadrature algorithm is recursively applied to these. Both variants of subdivision are considered in this paper.

This paper describes the use of interval arithmetic to bound errors in an experiment for determining Newton's constant of gravitation. Using verified Gaussian quadrature we were able to assess the numerical errors as well as the effect of several tolerances in the physical experiment.

In this paper we describe the use of interval arithmetic in an experiment for determining G, Newton's constant of gravitation. Using an interval version of Gaussian quadrature, we bound the effects of numerical errors and of several tolerances in the physical experiment. This allowed to idientify “critical” tolerances which must be reduced in order to obtain G with the desired accuracy.