Truncation dimension for function approximation

Peter Kritzer; Friedrich Pillichshammer; Grzegorz W. Wasilkowski

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

Truncation dimension for function approximation

Peter Kritzer, Friedrich Pillichshammer, Grzegorz W. Wasilkowski

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

4 Scopus citations

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 dim^trnc(ε, s) of variables. Here ε is the error demand and we refer to dim^trnc(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.

Original language	English
Title of host publication	Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan
Pages	771-792
Number of pages	22
ISBN (Electronic)	9783319724560
DOIs	https://doi.org/10.1007/978-3-319-72456-0_34
State	Published - May 23 2018

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© Springer International Publishing AG, part of Springer Nature 2018. All rights reserved.

ASJC Scopus subject areas

General Mathematics

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

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Truncation dimension for function approximation

Abstract

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