Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (4): 1033-1052.doi: 10.1007/s10473-019-0409-x

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(S, T)-WEAK TRACTABILITY OF MULTIVARIATE LINEAR PROBLEMS IN THE AVERAGE CASE SETTING

Yongping LIU1, Guiqiao XU2   

  1. 1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;
    2. Department of Mathematics, Tianjin Normal University, Tianjin 300387, China
  • Received:2017-10-24 Revised:2018-07-02 Online:2019-08-25 Published:2019-09-12
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (11471043, 11671271) and the Beijing Natural Science Foundation (1172004).

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

CLC Number: 

  • 41A63
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