Reduced Basis Greedy Selection Using Random Training Sets

DOI10.1051/m2an/2020004zbMath1444.62113arXiv1810.09344OpenAlexW2999070312MaRDI QIDQ3304879

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Publication date: 3 August 2020

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.09344

zbMATH Keywords

random samplingentropy numbersKolmogorov \(n\)-widthsreduced basesperformance boundssparse high-dimensional polynomial approximation

Mathematics Subject Classification ID

Computational learning theory (68Q32) Algorithmic information theory (Kolmogorov complexity, etc.) (68Q30) Numerical interpolation (65D05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Rate of convergence, degree of approximation (41A25) Complexity and performance of numerical algorithms (65Y20) Manifolds of mappings (58D15) Neural nets and related approaches to inference from stochastic processes (62M45)

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Cites Work

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• ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
• Convergence Rates for Greedy Algorithms in Reduced Basis Methods
• Multivariate Approximation in Downward Closed Polynomial Spaces
• Approximation of high-dimensional parametric PDEs
• Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

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