TY - THES
A1 - Kostiuk, Anton
T1 - Multilevel Constructions
N2 - 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.
Y1 - 2014
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3942
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-39422
N1 - 2. Gutachter der Dissertation:
Prof. Dr. Ömür Uğur,
Middle East Technical University
ER -