884 research outputs found
Some Results on the Complexity of Numerical Integration
This is a survey (21 pages, 124 references) written for the MCQMC 2014
conference in Leuven, April 2014. We start with the seminal paper of Bakhvalov
(1959) and end with new results on the curse of dimension and on the complexity
of oscillatory integrals. Some small errors of earlier versions are corrected
Hot new directions for quasi-Monte Carlo research in step with applications
This article provides an overview of some interfaces between the theory of
quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC
theoretical settings: first order QMC methods in the unit cube and in
, and higher order QMC methods in the unit cube. One important
feature is that their error bounds can be independent of the dimension
under appropriate conditions on the function spaces. Another important feature
is that good parameters for these QMC methods can be obtained by fast efficient
algorithms even when is large. We outline three different applications and
explain how they can tap into the different QMC theory. We also discuss three
cost saving strategies that can be combined with QMC in these applications.
Many of these recent QMC theory and methods are developed not in isolation, but
in close connection with applications
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