On the necessity of low-effective dimension

Shu Tezuka

Research output: Contribution to journalArticle

6 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 languageEnglish
Pages (from-to)710-721
Number of pages12
JournalJournal of Complexity
Volume21
Issue number5
DOIs
Publication statusPublished - Oct 2005

Fingerprint

Effective Dimension
Quasi-Monte Carlo
Higher Dimensions
Convergence Rate
High-dimensional
Necessity
Class

All Science Journal Classification (ASJC) codes

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

Cite this

On the necessity of low-effective dimension. / Tezuka, Shu.

In: Journal of Complexity, Vol. 21, No. 5, 10.2005, p. 710-721.

Research output: Contribution to journalArticle

Tezuka, Shu. / On the necessity of low-effective dimension. In: Journal of Complexity. 2005 ; Vol. 21, No. 5. pp. 710-721.
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