On the randomized complexity of Banach space valued integration

DOI10.4064/SM223-3-2zbMath1310.65026arXiv1312.3290OpenAlexW2963005190MaRDI QIDQ2926672

Stefan Heinrich, Aicke Hinrichs

Publication date: 3 November 2014

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.3290

zbMATH Keywords

randomized algorithmsoptimal convergenceBanach space-valued integrationcomplexity of integrationmultilevel Monte Carlo algorithmBanach space of equal norm typeminimal error of integration

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Local theory of Banach spaces (46B07) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Complexity and performance of numerical algorithms (65Y20) Applications of functional analysis in numerical analysis (46N40)

Cites Work

• Tractability of multivariate problems. Volume II: Standard information for functionals.
• Deterministic and stochastic error bounds in numerical analysis
• Nonreflexive spaces of type 2
• On the type and cotype of Banach spaces
• Monte Carlo approximation of weakly singular integral operators
• The randomized information complexity of elliptic PDE
• Complexity of Banach Space Valued and Parametric Integration
• Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach
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