(s,lnκ)-weak tractability of linear problems

A. Papageorgiou, I. Petras, H. Woźniakowski

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We introduce a new notion of tractability for multivariate problems, namely (s,lnκ)-weak tractability for positive s and κ. This allows us to study the information complexity of a d-variate problem with respect to different powers of d and the bits of accuracy lnε−1. We consider the worst case error for the absolute and normalized error criteria. We provide necessary and sufficient conditions for (s,lnκ)-weak tractability for general linear problems and linear tensor product problems defined over Hilbert spaces. In particular, we show that non-trivial linear tensor product problems cannot be (s,lnκ)-weakly tractable when s∈(0,1] and κ∈(0,1]. On the other hand, they are (s,lnκ)-weakly tractable for κ<1 and s<1 if the univariate eigenvalues of the linear tensor product problem enjoy a polynomial decay. Finally, we study (s,lnκ)-weak tractability for the remaining combinations of the values of s and κ.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalJournal of Complexity
Volume40
DOIs
StatePublished - Jun 1 2017

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics(all)
  • Control and Optimization
  • Applied Mathematics

Keywords

  • Complexity
  • Multivariate problem
  • Tractability

Fingerprint Dive into the research topics of '(s,ln<sup>κ</sup>)-weak tractability of linear problems'. Together they form a unique fingerprint.

Cite this