On tractability of linear tensor product problems for ∞-variate classes of functions

G. W. Wasilkowski

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


We study tractability of linear tensor product problems defined on special Banach spaces of ∞-variate functions. In these spaces, functions have a unique decomposition f=Σufu with f u∈Hu, where u are finite subsets of N+ and Hu are Hilbert spaces of functions with variables listed in u. The norm of f is defined by the ℓq norm of {γu -1-fu-Hu:u⊂ℕ}, where γu's are given weights and q∈[1,∞]. We derive sufficient and necessary conditions for the problem to be tractable. These conditions are expressed in terms of the properties of the weights γu, the value of q, and the complexity of the corresponding problem for univariate functions. The previous results were obtained only for the Hilbert case of q=2 and dealt with weighted integration and weighted L 2-approximation.

Original languageEnglish
Pages (from-to)351-369
Number of pages19
JournalJournal of Complexity
Issue number5
StatePublished - Oct 2013


  • Tensor product problems
  • Tractability

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • General Mathematics
  • Control and Optimization
  • Applied Mathematics


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