Vortrag
Modified component-by-component constructions of (polynomial) lattice points
Vortrag von Prof. Dr. Peter Kritzer
Datum: 14.03.18 Zeit: 16.15 - 17.45 Raum: Y27H25
The (fast) component-by-component construction of lattice point sets and polynomial lattice point sets is a powerful method to obtain quadrature rules for approximating integrals over the d-dimensional unit cube. In this talk, we present modifications of the component-by-component algorithm and of the more recent successive coordinate search algorithm, which yield savings of the construction cost for lattice rules and polynomial lattice rules in weighted function spaces. The idea is to reduce the size of the search space for coordinates which are associated with small weights and are therefore of less importance to the overall error compared to coordinates associated with large weights. We analyze tractability conditions of the resulting quasi-Monte Carlo rules, and show some numerical results. The talk is based on joint work with J. Dick (UNSW Sydney), A. Ebert (KU Leuven), G. Leobacher (KFU Graz), and F. Pillichshammer (JKU Linz).