Gauss-type quadrature rules for rational functions
Classical Analysis and ODEs
2025-10-20 v1 Numerical Analysis
Numerical Analysis
Abstract
When integrating functions that have poles outside the interval of integration, but are regular otherwise, it is suggested that the quadrature rule in question ought to integrate exactly not only polynomials (if any), but also suitable rational functions. The latter are to be chosen so as to match the most important poles of the integrand. We describe two methods for generating such quadrature rules numerically and report on computational experience with them.
Cite
@article{arxiv.math/9307223,
title = {Gauss-type quadrature rules for rational functions},
author = {Walter Gautschi},
journal= {arXiv preprint arXiv:math/9307223},
year = {2025}
}