Necessity of low effective dimension
نویسنده
چکیده
Practitioners have long noticed that quasi-Monte Carlo methods work very well on functions that are nearly superpositions of low dimensional functions. The reason is that the low dimensional coordinate projections of QMC rules can have very good equidistribution properties at sample sizes for which the original rule itself cannot have good equidistribution. This paper explores a converse proposal: that low effective dimension is necessary for QMC to be much better than MC in high dimensions with practical sample sizes.
منابع مشابه
On the necessity of low-effective dimension
We introduce a class of functions in high dimensions which have themaximum effective dimension, then prove that generalized Sobol’sequences provide theO(N−1) convergence rate for the integration of this class of functions. An important consequence is that high-dimensional problems for which quasi-Monte Carlo outperforms Monte Carlo are not necessarily of low-effective dimension. © 2005 Elsevier...
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