On the necessity of low-effective dimension

Shu Tezuka

研究成果: ジャーナルへの寄稿記事

7 引用 (Scopus)

抜粋

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.

元の言語英語
ページ(範囲)710-721
ページ数12
ジャーナルJournal of Complexity
21
発行部数5
DOI
出版物ステータス出版済み - 10 2005

    フィンガープリント

All Science Journal Classification (ASJC) codes

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

これを引用