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Numerical integration is encountered in all fields of numerical analysis andthe engineering sciences. By now, various efficient and accurate quadraturerules are known; for instance, Gauss-type quadrature rules. In manyapplications, however, it might be impractical---if not even impossible---toobtain data to fit known quadrature rules. Often, experimental measurements areperformed at equidistant or even scattered points in space or time. In thiswork, we propose stable high order quadrature rules for experimental data,which can accurately handle general weight functions.

Stable High Order Quadrature Rules for Scattered Data and General Weight Functions