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2024 | OriginalPaper | Chapter

Infinite-Variate \(L^2\)-Approximation with Nested Subspace Sampling

Authors : Kumar Harsha, Michael Gnewuch, Marcin Wnuk

Published in: Monte Carlo and Quasi-Monte Carlo Methods

Publisher: Springer International Publishing

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Abstract

We consider \(L^2\)-approximation on weighted reproducing kernel Hilbert spaces of functions depending on infinitely many variables. We focus on unrestricted linear information, admitting evaluations of arbitrary continuous linear functionals. We distinguish between ANOVA and non-ANOVA spaces, where, by ANOVA spaces, we refer to function spaces whose norms are induced by an underlying ANOVA function decomposition. In ANOVA spaces, we provide an optimal algorithm to solve the approximation problem using linear information. We determine the upper and lower error bounds on the polynomial convergence rate of n-th minimal worst-case errors, which match if the weights decay regularly. For non-ANOVA spaces, we also establish upper and lower error bounds. Our analysis reveals that for weights with a regular and moderate decay behavior, the convergence rate of n-th minimal errors is strictly higher in ANOVA than in non-ANOVA spaces.

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previous chapter Simple Stratified Sampling for Simulating Multi-dimensional Markov Chains
next chapter Randomized Complexity of Vector-Valued Approximation
Appendix
Available only for authorised users
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Metadata
Title
Infinite-Variate -Approximation with Nested Subspace Sampling
Authors
Kumar Harsha
Michael Gnewuch
Marcin Wnuk
Copyright Year
2024
Book
Monte Carlo and Quasi-Monte Carlo Methods

Print ISBN: 978-3-031-59761-9

Electronic ISBN: 978-3-031-59762-6

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-59762-6_16

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