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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: 
Publication status: published
KU Leuven publication type: IMa
Appears in Collections:Numerical Analysis and Applied Mathematics Section
# (joint) last author

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