Truncation in average and worst case settings for special classes of ∞-variate functions

Peter Kritzer, Friedrich Pillichshammer, G. W. Wasilkowski

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The paper considers truncation errors for functions of the form f(x1,x2,…)=g(∑j=1 xjξj), i.e., errors of approximating f by fk(x1,…,xk)=g(∑j=1 kxjξj), where the numbers ξj converge to zero sufficiently fast and xj’s are i.i.d. random variables. As explained in the introduction, functions f of the form above appear in a number of important applications. To have positive results for possibly large classes of such functions, the paper provides bounds on truncation errors in both the average and worst case settings. The bounds are sharp in two out of three cases that we consider. In the former case, the functions g are from a Hilbert space G endowed with a zero mean probability measure with a given covariance kernel. In the latter case, the functions g are from a reproducing kernel Hilbert space, or a space of functions satisfying a Hölder condition.

Original languageEnglish
Pages (from-to)52-65
Number of pages14
JournalMathematics and Computers in Simulation
StatePublished - Jul 2019

Bibliographical note

Publisher Copyright:
© 2018 International Association for Mathematics and Computers in Simulation (IMACS)


  • Average case error
  • Covariance kernel
  • Dimension truncation
  • Reproducing kernel
  • Worst case error

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics


Dive into the research topics of 'Truncation in average and worst case settings for special classes of ∞-variate functions'. Together they form a unique fingerprint.

Cite this