Computational Mathematics and Statistics Seminar with Onyekachi Osisiogu: Construction Methods for Rank-1 Lattice Rules
Speaker: Onyekachi Osisiogu, Postdoctoral Researcher, Department of Applied Mathematics, Illinois Tech
Title: Construction Methods for Rank-1 Lattice Rules
Abstract: Lattice rules are quasi-Monte Carlo rules for approximating integrals over the s-dimensional unit cube. For dimensions s > 2, no explicit constructions are known such that one usually has to resort to computer search algorithms. In this talk, we consider search algorithms for constructing point sets of high-quality quasi-Monte Carlo methods. In particular, we study the construction of rank-1 lattice rules, where it is specified by a generating vector for numerical integration in weighted function spaces such as Korobov space. These construction schemes generate QMC point sets that achieve almost optimal error convergence rates in the function space. We show that the obtained error estimates become independent of the dimension under certain conditions on the weights, which are incorporated in the definition of the considered function space. Consequently, the integration problem becomes tractable. Furthermore, we derive fast implementations of the construction algorithms and confirm our theoretical findings with numerical results and experiments.
Meeting ID: 869 9001 6572
Computational Mathematics and Statistics SeminarZoom Link