Efficient multivariate approximation with transformed rank-1 lattices
Seiten
2022
Universitätsverlag Chemnitz
978-3-96100-161-3 (ISBN)
Universitätsverlag Chemnitz
978-3-96100-161-3 (ISBN)
We study the approximation of functions defined on different domains by trigonometric and transformed trigonometric functions. We investigate which of the many results known from the approximation theory on the d-dimensional torus can be transfered to other domains. We define invertible parameterized transformations and prove conditions under which functions from a weighted Sobolev space can be transformed into functions defined on the torus, that still have a certain degree of Sobolev smoothness and for which we know worst-case upper error bounds. By reverting the initial change of variables we transfer the fast algorithms based on rank-1 lattices used to approximate functions on the torus efficiently over to other domains and obtain adapted FFT algorithms.
Erscheinungsdatum | 05.01.2023 |
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Zusatzinfo | Diagramme |
Verlagsort | Chemnitz |
Sprache | englisch |
Maße | 148 x 210 mm |
Gewicht | 168 g |
Themenwelt | Mathematik / Informatik ► Mathematik |
Schlagworte | ank-1 lattice • Approximationstheorie • Change of variables • high-dimensional approximation Rang-1 Gitter • Hochdimensionale Approximation • Koordinatentransformation • Numerische Mathematik |
ISBN-10 | 3-96100-161-8 / 3961001618 |
ISBN-13 | 978-3-96100-161-3 / 9783961001613 |
Zustand | Neuware |
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