Set of anti-Gaussian quadrature rules for the optimal set of quadrature rules in Borges' sense

Abstract

Anti-Gaussian quadrature rules, introduced by Laurie in [1], have the property that their error is equal in magnitude but of the opposite sign to the corresponding Gaussian quadrature rules. Guided by that idea, we define and analyse the set of anti-Gaussian quadrature rules for the optimal set of quadrature rules in Borges' sense (see [2]), with respect to the set of r different weight functions. Also, we introduce the set of averaged quadrature rules and give some numerical examples.