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Acta Mathematica Scientia

, Volume 39, Issue 4, pp 1033–1052 | Cite as

(S, T)-Weak Tractability of Multivariate Linear Problems in the Average Case Setting

  • Yongping Liu (刘永平)Email author
  • Guiqiao Xu (许贵桥)Email author
Article
  • 12 Downloads

Abstract

The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case setting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s, t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s, t)-weak tractability of a multivariate approximation problem.

Key words

(s, t)-weak tractability linear problem linear tensor product problem Hilbert space average case setting 

2010 MR Subject Classification

41A63 65Y20 68Q25 

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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesBeijing Normal UniversityBeijingChina
  2. 2.Department of MathematicsTianjin Normal UniversityTianjinChina

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