On the necessity of low-effective dimension

Shu Tezuka

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)710-721
Number of pages12
JournalJournal of Complexity
Volume21
Issue number5
DOIs
Publication statusPublished - 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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