Truncation dimension for linear problems on multivariate function spaces

Aicke Hinrichs, Peter Kritzer, Friedrich Pillichshammer, G. W. Wasilkowski

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The paper considers linear problems on weighted spaces of multivariate functions of many variables. The main questions addressed are the following: when is it possible to approximate the solution for the original function of very many variables by the solution for the same function, however with all but the first k variables set to zero, so that the corresponding error is small? What is the truncation dimension, i.e., the smallest number k = k(ε) such that the corresponding error is bounded by a given error demand ε? Surprisingly, k(ε) could be very small even for weights with a modest speed of convergence to zero.

Original languageEnglish
Pages (from-to)661-685
Number of pages25
JournalNumerical Algorithms
Issue number2
StatePublished - Feb 6 2019

Bibliographical note

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.


  • Multivariate problems
  • Truncation algorithms
  • Truncation dimension
  • Weighted function spaces

ASJC Scopus subject areas

  • Applied Mathematics


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