Algorithm 973

Abstract

We present a numerical procedure to approximate integrals of the form ∫ b a f ( x ) dx , where f is a function with singularities close to, but outside the interval [ a , b ], with − ∞ ⩽ a < b ⩽ +∞. The algorithm is based on rational interpolatory Fejér 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 M atlab program.