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Fast, exact and stable reconstruction of multivariate algebraic polynomials in Chebyshev form

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.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-qucosa-160992
Date16 February 2015
CreatorsPotts, Daniel, Volkmer, Toni
ContributorsTU Chemnitz, Fakultät für Mathematik
PublisherUniversitätsbibliothek Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:preprint
Formatapplication/pdf, text/plain, application/zip
Relationdcterms:isPartOf:Preprintreihe der Fakultät für Mathematik der TU Chemnitz, Preprint 2015-03

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