A unified framework for the computation of polynomial quadrature weights and errors

Abstract

For the class of polynomial quadrature rules we show that conveniently chosen bases allow to compute both the weights and the theoretical error expression of a $n$-point rule via the undetermined coefficients method. As an illustration, the framework is applied to some classical rules such as Newton-Cotes, Adams-Bashforth, Adams-Moulton and Gaussian rules.