Error bounds for the integration of singular functions using equidistributed sequences

We consider integral approximations using equidistributed point sequences, which converge for Riemann integrable functions. Under certain conditions, Sobol (Soviet Math. Dokl. 14 (1973) 734) and Klinger (Computing 59 (1997) 223) showed convergence for some classes of singular functions. We focus on asymptotic error bounds and give a scheme for extensions of Sobol's results, thereby obtaining insight in the asymptotic error structure. Numerical examples are presented, validating the principle of "ignoring the singularity" and illustrating the use of extrapolation. (C) 2003 Elsevier Science (USA). All rights reserved.