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

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

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