Exact cubature for a class of functions of maximum effective dimension

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. Key words: ANOVA, antisymmetric functions, effective dimension, high dimensional integrals

• Type: Journal
• Year: 2006
• Where: JC
• Authors: Shu Tezuka, Anargyros Papageorgiou
• Keywords: Dimension, Effective Dimension, JC 2006, Worst Case Error