Tractability of Approximation in the Weighted Korobov Space in the Worst-Case Setting

Adrian Ebert (), Peter Kritzer () and Friedrich Pillichshammer ()
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Adrian Ebert: Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics (RICAM)
Peter Kritzer: Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics (RICAM)
Friedrich Pillichshammer: Johannes Kepler Universität Linz, Institut für Finanzmathematik und Angewandte Zahlentheorie

A chapter in Advances in Modeling and Simulation, 2022, pp 131-150 from Springer

Abstract: Abstract In this paper we consider $$L_p$$ L p -approximation, $$p \in \{2,\infty \}$$ p ∈ { 2 , ∞ } , of periodic functions from weighted Korobov spaces. In particular, we discuss tractability properties of such problems, which means that we aim to relate the dependence of the information complexity on the error demand $$\varepsilon $$ ε and the dimension d to the decay rate of the weight sequence $$(\gamma _j)_{j \ge 1}$$ ( γ j ) j ≥ 1 assigned to the Korobov space. Some results have been well known since the beginning of this millennium, others have been proven quite recently. We give a survey of these findings and will add some new results on the $$L_\infty $$ L ∞ -approximation problem. To conclude, we give a concise overview of results and collect a number of interesting open problems.

Keywords: Approximation; Worst-case error; Average-case error; Tractability; Weighted Korobov space (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-10193-9_7

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DOI: 10.1007/978-3-031-10193-9_7

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