A Deterministic Algorithm for Constructing Multiple Rank-1 Lattices of Near-Optimal Size

21 Mar 2020 Gross Craig Iwen Mark A. Kämmerer Lutz Volkmer Toni

In this paper we present the first known deterministic algorithm for the construction of multiple rank-1 lattices for the approximation of periodic functions of many variables. The algorithm works by converting a potentially large reconstructing single rank-1 lattice for some $ d $-dimensional frequency set $ I \subset [N]^d $ into a collection of much smaller rank-1 lattices which allow for accurate and efficient reconstruction of trigonometric polynomials with coefficients in $ I $ (and, therefore, for the approximation of multivariate periodic functions)... (read more)

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