Small superposition dimension and active set construction for multivariate integration under modest error demand

A. D. Gilbert, G. W. Wasilkowski

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Constructing active sets is a key part of the Multivariate Decomposition Method. An algorithm for constructing optimal or quasi-optimal active sets is proposed in the paper. By numerical experiments, it is shown that the new method can provide sets that are significantly smaller than the sets constructed by the already existing method. The experiments also show that the superposition dimension could surprisingly be very small, at most 3, when the error demand is not smaller than 10−3 and the weights decay sufficiently fast.

Original languageEnglish
Pages (from-to)94-109
Number of pages16
JournalJournal of Complexity
Volume42
DOIs
StatePublished - Oct 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.

Keywords

  • Active set
  • Infinite-variate integration
  • Multivariate Decomposition Method
  • Numerical integration
  • Superposition dimension

ASJC Scopus subject areas

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

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