On the approximate evaluation of Hadamard finite-part integrals

Grunwald's algorithms for the numerical evaluation of Hadamard finite-part integrals with non-integer exponent are extended to the case of integer exponent. These algorithms are based on the use of Bernstein polynomials and it is shown how, by an appropriate modification of the first algorithm, a convergence rate of order 1/N 2 may be obtained, where N is the number of function evaluations.