On equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in L1 or L∞

M. Hefter; K. Ritter; G. W. Wasilkowski

doi:10.1016/j.jco.2015.07.001

On equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in L₁ or L_∞

M. Hefter, K. Ritter, G. W. Wasilkowski

Computer Science

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

16 Scopus citations

Abstract

We consider weighted anchored and ANOVA spaces of functions with mixed first order partial derivatives bounded in L₁ or L_∞ norms. We provide conditions on the weights under which the corresponding spaces have equivalent norms with constants independent of, or only polynomially dependent on the number of variables.

Original language	English
Pages (from-to)	1-19
Number of pages	19
Journal	Journal of Complexity
Volume	32
Issue number	1
DOIs	https://doi.org/10.1016/j.jco.2015.07.001
State	Published - Feb 1 2016

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

ANOVA decomposition
Anchored decomposition
Embeddings
Equivalence of norms
Tractability
Weighted function spaces

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.2015.07.001

Cite this

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KW - Embeddings

KW - Equivalence of norms

KW - Tractability

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