A fast numerical algorithm for the integration of rational functions

Abstract. A new iterative method for numerical integration of rational func-tions on the real line is presented. The algorithm transforms the rational in-tegrand into a new rational function preserving the integral on the line. The coefficients of the new function are explicit polynomials in the original ones. These transformations depend on the degree of the input and the desired order of the method. Both parameters are arbitrary. The formulas can be precom-puted. Iteration yields an approximation of the desired integral with m-th order convergence. Examples illustrating the automatic generation of these formulas and the numerical behaviour of this method are given. 1