Embeddings for infinite-dimensional integration and L2-approximation with increasing smoothness

M. Gnewuch; M. Hefter; A. Hinrichs; K. Ritter; G. W. Wasilkowski

doi:10.1016/j.jco.2019.04.002

Embeddings for infinite-dimensional integration and L₂-approximation with increasing smoothness

M. Gnewuch, M. Hefter, A. Hinrichs, K. Ritter, G. W. Wasilkowski

Computer Science

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We study integration and L₂-approximation on countable tensor products of function spaces of increasing smoothness. We obtain upper and lower bounds for the minimal errors, which are sharp in many cases including, e.g., Korobov, Walsh, Haar, and Sobolev spaces. For the proofs we derive embedding theorems between spaces of increasing smoothness and appropriate weighted function spaces of fixed smoothness.

Original language	English
Article number	101406
Journal	Journal of Complexity
Volume	54
DOIs	https://doi.org/10.1016/j.jco.2019.04.002
State	Published - Oct 2019

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

Embedding theorems
High-dimensional integration
Infinite-dimensional integration
Reproducing kernel Hilbert spaces
Tractability

ASJC Scopus subject areas

Algebra and Number Theory
Statistics and Probability
Numerical Analysis
General Mathematics
Control and Optimization
Applied Mathematics

Access to Document

10.1016/j.jco.2019.04.002

Cite this

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AU - Hefter, M.

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AU - Ritter, K.

AU - Wasilkowski, G. W.

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KW - Reproducing kernel Hilbert spaces

KW - Tractability

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