Monte Carlo methods for uniform approximation on periodic Sobolev spaces with mixed smoothness

DC FieldValueLanguage
dc.contributor.authorByrenheid, Glenn
dc.contributor.authorKunsch, Robert J.
dc.contributor.authorVan Kien Nguyen
dc.date.accessioned2021-12-23T16:16:16Z-
dc.date.available2021-12-23T16:16:16Z-
dc.date.issued2018
dc.identifier.issn0885064X
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/11801-
dc.description.abstractWe consider the order of convergence for linear and nonlinear Monte Carlo approximation of compact embeddings from Sobolev spaces of dominating mixed smoothness with integrability 1 < p < infinity defined on the torus T-d into the space L-infinity (T-d) via methods that use arbitrary linear information. These cases are interesting because we can gain a speedup of up to 1/2 in the main rate compared to deterministic approximation. In doing so we determine the rate for some cases that have been left open by Fang and Duan (2007, 2008). (C) 2017 Elsevier Inc. All rights reserved.
dc.description.sponsorshipGerman Research Foundation (DFG)German Research Foundation (DFG) [U1-403/2-1]; Emmy-Noether programmeGerman Research Foundation (DFG) [U1-403/1-1]; DFG Research Training GroupGerman Research Foundation (DFG) [1523]; DFGGerman Research Foundation (DFG)European Commission [1324]; The authors thank the organizers of the conference ``IBC on the 70th anniversary of Henryk Wozniakowski'' where this project has been initiated. G.B. gratefully acknowledges support by the German Research Foundation (DFG) U1-403/2-1 and the Emmy-Noether programme, U1-403/1-1. R.J.K. acknowledges support from the DFG Research Training Group 1523, and the DFG-priority program 1324. V. K. Nguyen wishes to thank the DFG-priority program 1324 for financial support. Finally the authors would like to thank the two referees for a careful reading and various valuable hints to improve the paper.
dc.language.isoen
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE
dc.relation.ispartofJOURNAL OF COMPLEXITY
dc.subjectComputer Science
dc.subjectComputer Science, Theory & Methods
dc.subjectInformation-based complexity
dc.subjectLinear information
dc.subjectMathematics
dc.subjectMathematics, Applied
dc.subjectMixed periodic Sobolev spaces
dc.subjectMonte Carlo approximation
dc.subjectNUMBERS
dc.subjectOrder of convergence
dc.titleMonte Carlo methods for uniform approximation on periodic Sobolev spaces with mixed smoothness
dc.typejournal article
dc.identifier.doi10.1016/j.jco.2017.12.002
dc.identifier.isiISI:000429389900005
dc.description.volume46
dc.description.startpage90
dc.description.endpage102
dc.contributor.orcid0000-0003-1039-6283
dc.contributor.orcid0000-0003-0835-9870
dc.contributor.researcheridAAO-5127-2020
dc.identifier.eissn10902708
dc.publisher.place525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
dcterms.isPartOf.abbreviationJ. Complex.
dcterms.oaStatusGreen Submitted
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