Lutz Kämmerer: Multiple Rank-1 Lattices as Sampling Schemes for Multivariate Trigonometric Polynomials

Author(s):

Lutz Kämmerer

Title:

Lutz Kämmerer: Multiple Rank-1 Lattices as Sampling Schemes for Multivariate Trigonometric Polynomials

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 11, 2015

Mathematics Subject Classification:

    65T40 []
    65T50 []

Abstract:

We present a new sampling method that allows the unique reconstruction of (sparse) multivariate trigonometric polynomials. The crucial idea is to use several rank-1 lattices as spatial discretization in order to overcome limitations of a single rank-1 lattice sampling method. The structure of the corresponding sampling scheme allows for the fast computation of the evaluation and the reconstruction of multivariate trigonometric polynomials, i.e., a fast Fourier transform. Moreover, we present a first algorithm that constructs a reconstructing sampling scheme consisting of several rank-1 lattices for a given frequency index set. Various numerical tests indicate the advantages of the constructed sampling schemes.

Keywords:

sparse multivariate trigonometric polynomials, lattice rule, multiple rank-1 lattice, fast Fourier transform

Language:

English

Publication time:

07/2015