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Daniel Potts, Toni Volkmer: Fast, exact and stable reconstruction of multivariate algebraic polynomials in Chebyshev form

Daniel Potts, Toni Volkmer: Fast, exact and stable reconstruction of multivariate algebraic polynomials in Chebyshev form


Author(s):
Daniel Potts
Toni Volkmer
Title:
Daniel Potts, Toni Volkmer: Fast, exact and stable reconstruction of multivariate algebraic polynomials in Chebyshev form
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 03, 2015
Mathematics Subject Classification:
    65T []
Abstract:
We describe a fast method for the evaluation of an arbitrary high-dimensional multivariate algebraic polynomial in Chebyshev form at the nodes of an arbitrary rank-1 Chebyshev lattice. Our main focus is on conditions on rank-1 Chebyshev lattices allowing for the exact reconstruction of such polynomials from samples along such lattices and we present an algorithm for constructing suitable rank-1 Chebyshev lattices based on a component-by-component approach. Moreover, we give a method for the fast, exact and stable reconstruction.
Keywords:
multivariate Chebyshev polynomials, reconstruction, rank-1 Chebyshev lattices, high-dimensional problems, hyperbolic cross, fast cosine transform
Language:
English
Publication time:
01/2015

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