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2024 | OriginalPaper | Chapter

QMC Strength for Some Random Configurations on the Sphere

Authors : Víctor de la Torre, Jordi Marzo

Published in: Monte Carlo and Quasi-Monte Carlo Methods

Publisher: Springer International Publishing

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Abstract

A sequence \((X_N)\subset \mathbb {S}^d\) of N-point sets from the d-dimensional sphere has QMC strength \(s^*>d/2\) if it has worst-case error of optimal order, \(N^{-s/d},\) for Sobolev spaces of order s for all \(d/2<s<s^*,\) and the order is not optimal for \(s> s^*.\) In [15] conjectured values of the strength are given for some well known point families in \(\mathbb S^2\) based on numerical results. We study the average QMC strength for some related random configurations.

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previous chapter Convergence of the Tamed-Euler–Maruyama Method for SDEs with Discontinuous and Polynomially Growing Drift

next chapter Multilevel MCMC with Level-Dependent Data in a Model Case of Structural Damage Assessment

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Title: QMC Strength for Some Random Configurations on the Sphere
Authors: Víctor de la Torre
Jordi Marzo
Publisher: Springer International Publishing
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_31

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