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Quantum Integration in Sobolev Classes

  • We study high dimensional integration in the quantum model of computation. We develop quantum algorithms for integration of functions from Sobolev classes \(W^r_p [0,1]^d\) and analyze their convergence rates. We also prove lower bounds which show that the proposed algorithms are, in many cases, optimal within the setting of quantum computing. This extends recent results of Novak on integration of functions from Hölder classes.

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Metadaten
Author:Stefan Heinrich
URN (permanent link):urn:nbn:de:hbz:386-kluedo-50632
Serie (Series number):Interner Bericht des Fachbereich Informatik (318)
Document Type:Report
Language of publication:English
Publication Date:2017/11/10
Year of Publication:2002
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/11/10
Number of page:28
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)