Multilevel Constructions
- The thesis consists of the two chapters. The first chapter is addressed to make a deep investigation of the MLMC method. In particular we take an optimisation view at the estimate. Rather than fixing the number of discretisation points \(n_i\) to be a geometric sequence, we are trying to find an optimal set up for \(n_i\) such that for a fixed error the estimate can be computed within a minimal time. In the second chapter we propose to enhance the MLMC estimate with the weak extrapolation technique. This technique helps to improve order of a weak convergence of a scheme and as a result reduce CC of an estimate. In particular we study high order weak extrapolation approach, which is know not be inefficient in the standard settings. However, a combination of the MLMC and the weak extrapolation yields an improvement of the MLMC.
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| Author: | Anton Kostiuk |
|---|---|
| URN: | urn:nbn:de:hbz:386-kluedo-39422 |
| Advisor: | Ralf Korn |
| Document Type: | Doctoral Thesis |
| Language of publication: | English |
| Date of Publication (online): | 2014/12/09 |
| Year of first Publication: | 2014 |
| Publishing Institution: | Technische Universität Kaiserslautern |
| Granting Institution: | Technische Universität Kaiserslautern |
| Acceptance Date of the Thesis: | 2014/10/13 |
| Date of the Publication (Server): | 2014/12/10 |
| Page Number: | X, 103 |
| Note: | 2. Gutachter der Dissertation:
Prof. Dr. Ömür Uğur,
Middle East Technical University |
| Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
| DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
| Licence (German): |  Standard gemäß KLUEDO-Leitlinien vom 28.10.2014 |