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