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

摘要

For the class of polynomial quadrature rules we show that conveniently chosenbases allow to compute both the weights and the theoretical error expression ofa $n$-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.