AGquad: a Matlab package for 1D and 2D anti-Gauss type rules

Abstract

Anti-Gauss formulae have attracted a great deal of interest in recent years. There are two main reasons for this. On the one hand, they make it possible to construct new rules, namely averaged or stratified formulae, which are characterized by a higher accuracy and a lower computational cost, compared to formulae with the same number of nodes. On the other hand, they provide numerical estimates of the error of the Gaussian rule for a fixed number of points. This allows one to determine the number of nodes required to achieve a prescribed accuracy in the integral approximation. In this paper, we provide a Matlab toolbox, including an interactive graphical user interface (GUI), to assist the interested researcher in performing the computation of 1D integrals using anti-Gauss formulae and one of their generalization. When coupled to Gauss rules, they lead to averaged and generalized averaged scheme, respectively. We also consider the computation of 2D integrals by Gauss/anti-Gauss rules.