A quadrature formula based on Chebyshev rational functions

Abstract

Several generalisations to the classical Gauss quadrature formulae have been developed over the last few years. When the integrand has singularities near the interval of integration, formulae based on rational functions give more accurate results than the classical quadrature rules based on polynomials. In this paper, we present one such generalisation which uses results from the theory of orthogonal rational functions. Compared to similar existing formulae, it has the advantage of improved stability and smaller quadrature weights.