An algorithm for the numerical evaluation of certain finite part integrals (Q420208)

Summary: Many algorithms that have been proposed for the numerical evaluation of Cauchy principal value integrals are numerically unstable. In this work we present some formulae to evaluate the known Gaussian quadrature rules for finite part integrals \(\int^{\ast b}_a w(x)(f(x)/(x - t)^r)dx, r = 1, 2, \dots\), and extend Clenshow's algorithm to evaluate these integrals in a stable way.