The set of anti-Gaussian quadrature rules and corresponding multiple orthogonal polynomials

Abstract

Laurie in ([1]) introduced anti-Gaussian quadrature rule, that gives an error equal in magnitude but of opposite sign to that of the corresponding Gaussian quadrature rule. Here, we consider a set of anti-Gaussian quadrature rules for the optimal set of quadrature rules in Borges’ sense, with respect to the set of r different weight functions, as well as the corresponding class of multiple orthogonal polynomials. Also, we define the set of averaged quadrature formulas and give some numerical examples.