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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| Author: | Stefan Heinrich |
|---|---|
| URN: | urn:nbn:de:hbz:386-kluedo-50632 |
| Series (Serial Number): | Interner Bericht des Fachbereich Informatik (318) |
| Document Type: | Report |
| Language of publication: | English |
| Date of Publication (online): | 2017/11/10 |
| Year of first Publication: | 2002 |
| Publishing Institution: | Technische Universität Kaiserslautern |
| Date of the Publication (Server): | 2017/11/10 |
| Page Number: | 28 |
| Faculties / Organisational entities: | Kaiserslautern - 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) |