Computing Discrepancies Related to Spaces of Smooth Periodic Functions

  • A notion of discrepancy is introduced, which represents the integration error on spaces of \(r\)-smooth periodic functions. It generalizes the diaphony and constitutes a periodic counterpart to the classical \(L_2\)-discrepancy as weil as \(r\)-smooth versions of it introduced recently by Paskov [Pas93]. Based on previous work [FH96], we develop an efficient algorithm for computing periodic discrepancies for quadrature formulas possessing certain tensor product structures, in particular, for Smolyak quadrature rules (also called sparse grid methods). Furthermore, fast algorithms of computing periodic discrepancies for lattice rules can easily be derived from well-known properties of lattices. On this basis we carry out numerical comparisons of discrepancies between Smolyak and lattice rules.

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Author:Karin Frank, Stefan Heinrich
URN (permanent link):urn:nbn:de:hbz:386-kluedo-49280
Serie (Series number):Interner Bericht des Fachbereich Informatik (286)
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:14
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)