Algorithm 973: Extended Rational Fejer Quadrature Rules Based on Chebyshev Orthogonal Rational Functions

摘要

We present a numerical procedure to approximate integrals of the form integral(b)(a) f (x)dx, where f is a function with singularities close to, but outside the interval [a, b], with -infinity <= a < b <= +infinity. The algorithm is based on rational interpolatory Fej ' er quadrature rules, together with a sequence of real and/or complex conjugate poles that are given in advance. Since for n fixed in advance, the accuracy of the computed nodes and weights in the n-point rational quadrature formula strongly depends on the given sequence of poles, we propose a small number of iterations over the number of points in the rational quadrature rule, limited by the value n (instead of fixing the number of points in advance) in order to obtain the best approximation among the first n. The proposed algorithm is implemented as a MATLAB program.