New methods for high-dimensional verified quadrature (Q1300081)

Rather than relying on conventional integration rules with remainder formulae to provide verified methods of integration, an approach with Taylor models is used. Rigorous bounds are calculated automatically while computing the integral itself using a local Taylor model. The method is especially successful for higher-dimensional quadratures with analytic integrands. Numerical examples with order up to ten and dimension up to eight are provided and the results compared with conventional methods. Typically only a modest number of subdivisions for the Taylor model was required to achieve high numerical accuracy.