Truncation Dimension for Function Approximation

Peter Kritzer (), Friedrich Pillichshammer () and Grzegorz W. Wasilkowski ()
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Peter Kritzer: Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics (RICAM)
Friedrich Pillichshammer: Johannes Kepler University Linz, Department of Financial Mathematics and Applied Number Theory
Grzegorz W. Wasilkowski: University of Kentucky, Computer Science Department

A chapter in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 2018, pp 771-792 from Springer

Abstract: Abstract We consider the approximation of functions of s variables, where s is very large or infinite, that belong to weighted anchored spaces. We study when such functions can be approximated by algorithms designed for functions with only very small number dimtrnc(ε, s) of variables. Here ε is the error demand and we refer to dimtrnc(ε, s) as the ε-truncation dimension. We show that for sufficiently fast decaying product weights and modest error demand (up to about ε ≈ 10−5) the truncation dimension is surprisingly very small.

Keywords: Truncation Dimension; Weight Products; Erratic Demand; ANOVA Decomposition; Worst Case Setting (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-72456-0_34

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DOI: 10.1007/978-3-319-72456-0_34

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