Numerical integration of singular integrands using low-discrepancy sequences (Q1377278)

This paper considers the integration error for quasi-Monte Carlo integration for functions on the \(s\)-dimensional unit cube with point singularities. For the \(s\)-dimensional Halton sequence, \({\mathbf x}_1, {\mathbf x}_2, \dots\), an asymptotic error bound is derived for the functions of type \(f({\mathbf x})=g({\mathbf x})/\{| {\mathbf x}^{(1)}| ^{\beta_1}+\cdots+| {\mathbf x}^{(s)}| ^{\beta_s}\}\) with positive \(\beta_i\) satisfying \(\sum_{i=1}^s (1/\beta_i)>1\) and \(g\) with bounded variation.