Exact cubature for a class of functions of maximum effective dimension

Shu Tezuka, Anargyros Papageorgiou

Research output: Contribution to journalArticle

Abstract

We consider high-dimensional integration in a broad class of functions where all elements have maximum effective dimension. We show that there exists an exact cubature with only two points. Therefore, not only the convergence but also the worst case error of quasi-Monte Carlo need not depend on the effective dimension at all.

Original languageEnglish
Pages (from-to)652-659
Number of pages8
JournalJournal of Complexity
Volume22
Issue number5
DOIs
Publication statusPublished - Jan 1 2006

Fingerprint

Effective Dimension
Cubature
Worst Case Error
Quasi-Monte Carlo
High-dimensional
Class

All Science Journal Classification (ASJC) codes

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

Cite this

Exact cubature for a class of functions of maximum effective dimension. / Tezuka, Shu; Papageorgiou, Anargyros.

In: Journal of Complexity, Vol. 22, No. 5, 01.01.2006, p. 652-659.

Research output: Contribution to journalArticle

Tezuka, Shu ; Papageorgiou, Anargyros. / Exact cubature for a class of functions of maximum effective dimension. In: Journal of Complexity. 2006 ; Vol. 22, No. 5. pp. 652-659.
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