%0 Journal Article
%T On the component by component construction of polynomial lattice point sets for numerical integration in weighted Sobolev spaces
%A Peter Kritzer
%A Friedrich Pillichshammer
%J Uniform Distribution Theory
%D 2011
%I Mathematical Institute of the Slovak Academy of Sciences
%X Polynomial lattice point sets are polynomial versions of classical lattice point sets and among the most widely used classes of node sets for quasi-Monte Carlo integration. In this paper, we study the worst-case integration error of digitally shifted polynomial lattice point sets and give step by step construction algorithms to obtain polynomial lattices that achieve a low worst-case error in certain weighted Sobolev spaces. The construction algorithm is a so-called component by component algorithm, choosing one component of the relevant point set at a time. Furthermore, under certain conditions on the weights, we achieve that there is only a polynomial or even no dependence of the worst-case error on the dimension of the integration problem.
%K Quasi-Monte Carlo
%K polynomial lattice rules
%K weighted Sobolev spaces
%K Hilbert space with kernel
%K Walsh function
%U http://www.boku.ac.at/MATH/udt/vol06/no1/7KritPill11-1.pdf