Title: Weighted QMC rules - Stop anywhere Authors: Nuyens, Dirk # Issue Date: Sep-2009 Conference: Dagstuhl Seminar on Algorithms and Complexity for Continuous Problems location:Schloss Dagstuhl, Wadern, Germany date:20-25 September 2009 Abstract: We study the worst case integration error of combinations of quadrature rules in a reproducing kernel Hilbert space. We show that the error, with respect to the total number $N$ of function evaluations used, cannot decrease faster than $O(N^{-1})$ for an equal-weight rule. However, if the errors of the quadrature rules constituting a compound rule have an order of convergence $O(N^{-\alpha})$ for $\alpha>1$ then, by introducing weights, this order of convergence can be shown to be recovered for the compound rule. The theory applies to lattice sequences as well as digital sequences. URI: http://www.dagstuhl.de/Materials/index.en.phtml?09391 Publication status: published KU Leuven publication type: IMa Appears in Collections: NUMA, Numerical Analysis and Applied Mathematics Section