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

Autor(en): Byrenheid, Glenn
Kunsch, Robert J.
Van Kien Nguyen
Stichwörter: Computer Science; Computer Science, Theory & Methods; Information-based complexity; Linear information; Mathematics; Mathematics, Applied; Mixed periodic Sobolev spaces; Monte Carlo approximation; NUMBERS; Order of convergence
Erscheinungsdatum: 2018
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: JOURNAL OF COMPLEXITY
Volumen: 46
Startseite: 90
Seitenende: 102
Zusammenfassung: 
We 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.
ISSN: 0885064X
DOI: 10.1016/j.jco.2017.12.002

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