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

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Yongping Liu  (刘永平)

  2. Department of Mathematics, Tianjin Normal University, Tianjin, 300387, China

    Guiqiao Xu  (许贵桥)

Authors
  1. Yongping Liu  (刘永平)
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  2. Guiqiao Xu  (许贵桥)
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Corresponding authors

Correspondence to Yongping Liu  (刘永平) or Guiqiao Xu  (许贵桥).

Additional information

This work was supported by the National Natural Science Foundation of China (11471043, 11671271) and the Beijing Natural Science Foundation (1172004).

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Liu, Y., Xu, G. (S, T)-Weak Tractability of Multivariate Linear Problems in the Average Case Setting. Acta Math Sci 39, 1033–1052 (2019). https://doi.org/10.1007/s10473-019-0409-x

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  • DOI: https://doi.org/10.1007/s10473-019-0409-x

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