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

Huichao Yan and Jia Chen ()
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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

Mathematics, 2024, vol. 12, issue 13, 1-20

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 .

Keywords: L 2 -approximation; information complexity; tractability; weighted Hilbert spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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