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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.

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Author:Karin Frank, Stefan Heinrich
URN (permanent link):urn:nbn:de:hbz:386-kluedo-49277
Serie (Series number):Interner Bericht des Fachbereich Informatik (284)
Document Type:Report
Language of publication:English
Publication Date:2017/10/24
Year of Publication:1996
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/10/24
Number of page:23
Faculties / Organisational entities: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)