Scaled lattice rules for integration on ${\mathbb{R}}^d$ achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spaces

Dirk Nuyens, Yuya Suzuki

We introduce a new method to approximate integrals ${\int }_{{\mathbb{R}}^d}f(\mathbf{x})\mathrm{d}\mathbf{x}$ which simply scales lattice rules from the unit cube $[0,1]^…