Computing Discrepancies of Smolyak Quadrature Rules
- In recent years, Smolyak quadrature rules (also called hyperbolic cross points or sparse grids) have gained interest as a possible competitor to number theoretic quadratures for high dimensional problems. A standard way of comparing the quality of multivariate quadrature formulas consists in computing their \(L_2\)-discrepancy. Especially for larger dimensions, such computations are a highly complex task. In this paper we develop a fast recursive algorithm for computing the \(L_2\)-discrepancy (and related quality measures) of general Smolyak quadratures. We carry out numerical comparisons between the discrepancies of certain Smolyak rules, Hammersley and Monte Carlo sequences.
Author: | Karin Frank, Stefan Heinrich |
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URN: | urn:nbn:de:hbz:386-kluedo-49277 |
Series (Serial Number): | Interner Bericht des Fachbereich Informatik (284) |
Document Type: | Report |
Language of publication: | English |
Date of Publication (online): | 2017/10/24 |
Year of first Publication: | 1996 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2017/10/24 |
Page Number: | 23 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Informatik |
DDC-Cassification: | 0 Allgemeines, Informatik, Informationswissenschaft / 004 Informatik |
Licence (German): | Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0) |