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Exponential Convergence-( t , s )-Weak Tractability of Approximation in Weighted Hilbert Spaces

Author

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  • Huichao Yan

    (School of Computer and Network Engineering, Shanxi Datong University, Datong 037009, China)

  • Jia Chen

    (School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China)

Abstract

We study L 2 -approximation problems in the weighted Hilbert spaces in the worst case setting. Three interesting weighted Hilbert spaces appear in this paper, whose weights are equipped with two positive parameters γ j and α j for j ∈ N . We consider algorithms using the class of arbitrary linear functionals. We discuss the exponential convergence- ( t , s ) -weak tractability of these L 2 -approximation problems. In particular, we obtain the sufficient and necessary conditions on the weights for exponential convergence-weak tractability and exponential convergence- ( t , 1 ) -weak tractability with t < 1 .

Suggested Citation

  • Huichao Yan & Jia Chen, 2024. "Exponential Convergence-( t , s )-Weak Tractability of Approximation in Weighted Hilbert Spaces," Mathematics, MDPI, vol. 12(13), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2067-:d:1427052
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    References listed on IDEAS

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    1. J. Rust & J. F. Traub & H. Wozniakowski, 2002. "Is There a Curse of Dimensionality for Contraction Fixed Points in the Worst Case?," Econometrica, Econometric Society, vol. 70(1), pages 285-329, January.
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