Convergence analysis and adaptive strategy for the certified quadrature over a set defined by inequalities

This paper investigates the sufficient conditions for the asymptotic convergence of a generic branch and prune algorithm dedicated to the verified quadrature of a function in several variables. Quadrature over domains defined by inequalities, and adaptive meshing strategies are in the scope of this analysis. The framework is instantiated using certified quadrature methods based on Taylor models (i.e. Taylor approximations with rigorously bounded remainder), and reported experiments confirmed the analysis. They also show that the performances of the instantiated algorithm are comparable with current methods for certified quadrature.