A unified framework for the computation of polynomial quadrature weights and errors
arXiv:1203.47955 citationsh-index: 5
Originality Synthesis-oriented
AI Analysis
Provides a unified computational approach for polynomial quadrature rules, but is incremental as it reformulates existing methods.
The paper presents a unified framework using undetermined coefficients to compute polynomial quadrature weights and error expressions, demonstrated on Newton-Cotes, Adams-Bashforth, Adams-Moulton, and Gaussian rules.
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.