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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-qucosa-160992 |
| Date | 16 February 2015 |
| Creators | Potts, Daniel, Volkmer, Toni |
| Contributors | TU Chemnitz, Fakultät für Mathematik |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint |
| Format | application/pdf, text/plain, application/zip |
| Relation | dcterms:isPartOf:Preprintreihe der Fakultät für Mathematik der TU Chemnitz, Preprint 2015-03 |
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