Truncation dimension for function approximation

Peter Kritzer, Friedrich Pillichshammer, Grzegorz W. Wasilkowski

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

4 Scopus citations


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.

Original languageEnglish
Title of host publicationContemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan
Number of pages22
ISBN (Electronic)9783319724560
StatePublished - May 23 2018

Bibliographical note

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

ASJC Scopus subject areas

  • General Mathematics


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