On the necessity of low-effective dimension

Shu Tezuka

doi:10.1016/j.jco.2005.05.004

On the necessity of low-effective dimension

Shu Tezuka

Division of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We introduce a class of functions in high dimensions which have the maximum effective dimension, then prove that generalized Sobol' sequences provide the O(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.

Original language	English
Pages (from-to)	710-721
Number of pages	12
Journal	Journal of Complexity
Volume	21
Issue number	5
DOIs	https://doi.org/10.1016/j.jco.2005.05.004
Publication status	Published - Oct 2005

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Statistics and Probability
Numerical Analysis
Mathematics(all)
Control and Optimization
Applied Mathematics

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10.1016/j.jco.2005.05.004

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title = "On the necessity of low-effective dimension",

abstract = "We introduce a class of functions in high dimensions which have the maximum effective dimension, then prove that generalized Sobol' sequences provide the O(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.",

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AB - We introduce a class of functions in high dimensions which have the maximum effective dimension, then prove that generalized Sobol' sequences provide the O(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.

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DO - 10.1016/j.jco.2005.05.004

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SP - 710

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JO - Journal of Complexity

JF - Journal of Complexity

IS - 5

ER -

On the necessity of low-effective dimension

Abstract

All Science Journal Classification (ASJC) codes

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