A note on equivalence of anchored and ANOVA spaces; lower bounds

Peter Kritzer; Friedrich Pillichshammer; G. W. Wasilkowski

doi:10.1016/j.jco.2016.06.001

A note on equivalence of anchored and ANOVA spaces; lower bounds

Peter Kritzer, Friedrich Pillichshammer, G. W. Wasilkowski

Computer Science

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

10 Scopus citations

Abstract

We provide lower bounds for the norms of embeddings between γ-weighted anchored and ANOVA spaces of s-variate functions on [0,1]^s with mixed partial derivatives of order one bounded in L_p norm (p∈[1,∞]). In particular we show that the norms behave polynomially in s for specific instances of finite order weights and finite diameter weights, and increase faster than any polynomial in s for product order-dependent weights.

Original language	English
Pages (from-to)	31-38
Number of pages	8
Journal	Journal of Complexity
Volume	38
DOIs	https://doi.org/10.1016/j.jco.2016.06.001
State	Published - Feb 1 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.

Keywords

ANOVA decomposition
Anchored decomposition
Embeddings
Equivalence of norms
Weighted function spaces

ASJC Scopus subject areas

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

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10.1016/j.jco.2016.06.001

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AU - Pillichshammer, Friedrich

AU - Wasilkowski, G. W.

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N2 - We provide lower bounds for the norms of embeddings between γ-weighted anchored and ANOVA spaces of s-variate functions on [0,1]s with mixed partial derivatives of order one bounded in Lp norm (p∈[1,∞]). In particular we show that the norms behave polynomially in s for specific instances of finite order weights and finite diameter weights, and increase faster than any polynomial in s for product order-dependent weights.

AB - We provide lower bounds for the norms of embeddings between γ-weighted anchored and ANOVA spaces of s-variate functions on [0,1]s with mixed partial derivatives of order one bounded in Lp norm (p∈[1,∞]). In particular we show that the norms behave polynomially in s for specific instances of finite order weights and finite diameter weights, and increase faster than any polynomial in s for product order-dependent weights.

KW - ANOVA decomposition

KW - Anchored decomposition

KW - Embeddings

KW - Equivalence of norms

KW - Weighted function spaces

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JO - Journal of Complexity

JF - Journal of Complexity

ER -

A note on equivalence of anchored and ANOVA spaces; lower bounds

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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