Internality of truncated averaged Gaussian quadratures

Abstract

When moments or modi ed moments of the weight function are difficult to compute, generalized averaged Gaussian quadratures can serve as good substitutes. These formulas were introduced by Spalević [3], where it was demonstrated that they may yield a smaller error compared to the Gauss quadrature rules. However, generalized averaged Gaussian quadratures may have external nodes. This would make them unusable when the domain of the integrand is limited to the convex hull of the support of the weight function. In this paper we investigate whether removing some of the last rows and columns of their Jacobi matrices (cf. [2]) will produce quadrature rules with no external nodes. The results that will be presented have been recently published in [1].