Exact cubature for a class of functions of maximum effective dimension

Shu Tezuka; Anargyros Papageorgiou

doi:10.1016/j.jco.2006.04.002

Exact cubature for a class of functions of maximum effective dimension

Shu Tezuka, Anargyros Papageorgiou

Division of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	652-659
Number of pages	8
Journal	Journal of Complexity
Volume	22
Issue number	5
DOIs	https://doi.org/10.1016/j.jco.2006.04.002
Publication status	Published - Oct 2006

All Science Journal Classification (ASJC) codes

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

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10.1016/j.jco.2006.04.002

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title = "Exact cubature for a class of functions of maximum effective dimension",

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.",

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AB - 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.

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Exact cubature for a class of functions of maximum effective dimension

Abstract

All Science Journal Classification (ASJC) codes

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