Journal
JOURNAL OF COMPLEXITY
Volume 31, Issue 4, Pages 617-636Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jco.2015.02.006
Keywords
Exponential convergence-tractability; Linear problem; Eigenvalue; Average case setting
Funding
- National Natural Science Foundation of China [11271263, 11471043]
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We study d-variate general linear problems defined over Hilbert spaces in the average case setting. We consider algorithms that use finitely many evaluations of arbitrary linear functionals. We obtain the necessary and sufficient conditions for Exponential Convergence-(Strong) Polynomial Tractability, Quasi-Polynomial Tractability and (Uniform) Weak Tractability. All results are in terms of the eigenvalues of the corresponding covariance operators. (C) 2015 Elsevier Inc. All rights reserved.
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