Convergence rates of high dimensional Smolyak quadrature
ESAIM: M2AN, 54 4 (2020) 1259-1307
Published online: 2020-06-18
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Domain Uncertainty Quantification for the Lippmann–Schwinger Volume Integral Equation
Fernando Henríquez and Ignacio Labarca-FigueroaSIAM/ASA Journal on Uncertainty Quantification 14 (1) 77 (2026)
https://doi.org/10.1137/24M1677782
Frequency-Explicit Shape Holomorphy in Uncertainty Quantification for Acoustic Scattering
R. Hiptmair, Ch. Schwab and E. A. SpenceSIAM/ASA Journal on Uncertainty Quantification 13 (4) 1904 (2025)
https://doi.org/10.1137/24M1688643
Helmholtz quasi-resonances are unstable under most single-signed perturbations of the wave speed
Euan A. Spence, Jared Wunsch and Yuzhou ZouJournal of Differential Equations 440 113441 (2025)
https://doi.org/10.1016/j.jde.2025.113441
Galerkin neural network-POD for acoustic and electromagnetic wave propagation in parametric domains
Philipp Weder, Mariella Kast, Fernando Henríquez and Jan S. HesthavenAdvances in Computational Mathematics 51 (4) (2025)
https://doi.org/10.1007/s10444-025-10245-9
Measure transport via polynomial density surrogates
Josephine Westermann and Jakob ZechFoundations of Data Science 7 (3) 838 (2025)
https://doi.org/10.3934/fods.2025001
Reduced basis method for the elastic scattering by multiple shape-parametric open arcs in two dimensions
José Pinto and Fernando HenríquezESAIM: Mathematical Modelling and Numerical Analysis 59 (1) 201 (2025)
https://doi.org/10.1051/m2an/2024078
Neural and spectral operator surrogates: unified construction and expression rate bounds
Lukas Herrmann, Christoph Schwab and Jakob ZechAdvances in Computational Mathematics 50 (4) (2024)
https://doi.org/10.1007/s10444-024-10171-2
Sparse moment quadrature for uncertainty modeling and quantification
Xuefei GuanReliability Engineering & System Safety 241 109665 (2024)
https://doi.org/10.1016/j.ress.2023.109665
Exploiting locality in sparse polynomial approximation of parametric elliptic PDEs and application to parameterized domains
Wouter Gerrit van Harten and Laura ScarabosioESAIM: Mathematical Modelling and Numerical Analysis 58 (5) 1581 (2024)
https://doi.org/10.1051/m2an/2024050
Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs
José Pinto, Fernando Henríquez and Carlos Jerez-HanckesJournal of Fourier Analysis and Applications 30 (2) (2024)
https://doi.org/10.1007/s00041-024-10071-5
The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs
Helmut Harbrecht, Marc Schmidlin and Christoph SchwabMathematical Models and Methods in Applied Sciences 34 (05) 881 (2024)
https://doi.org/10.1142/S0218202524500179
Multilevel Monte Carlo FEM for elliptic PDEs with Besov random tree priors
Christoph Schwab and Andreas SteinStochastics and Partial Differential Equations: Analysis and Computations 12 (3) 1574 (2024)
https://doi.org/10.1007/s40072-023-00313-w
Shape Uncertainty Quantification for Electromagnetic Wave Scattering via First-Order Sparse Boundary Element Approximation
Paul Escapil-Inchauspé and Carlos Jerez-HanckesIEEE Transactions on Antennas and Propagation 72 (8) 6627 (2024)
https://doi.org/10.1109/TAP.2024.3418199
A Filon-Clenshaw-Curtis-Smolyak rule for multi-dimensional oscillatory integrals with application to a UQ problem for the Helmholtz equation
Zhizhang Wu, Ivan Graham, Dingjiong Ma and Zhiwen ZhangMathematics of Computation 94 (354) 1911 (2024)
https://doi.org/10.1090/mcom/4007
Parametric Shape Holomorphy of Boundary Integral Operators with Applications
Jürgen Dölz and Fernando HenríquezSIAM Journal on Mathematical Analysis 56 (5) 6731 (2024)
https://doi.org/10.1137/23M1576451
2334 123 (2023)
https://doi.org/10.1007/978-3-031-38384-7_6
Коллокационная аппроксимация глубокими $\mathrm{ReLU}$-нейронными сетями решений параметрических и стохастических уравнений с частными производными c логнормальными входами
Dung DinhМатематический сборник 214 (4) 38 (2023)
https://doi.org/10.4213/sm9791
Sparse Polynomial Approximations for Affine Parametric Saddle Point Problems
Peng Chen and Omar GhattasVietnam Journal of Mathematics 51 (1) 151 (2023)
https://doi.org/10.1007/s10013-022-00584-1
Collocation approximation by deep neural ReLU networks for parametric and stochastic PDEs with lognormal inputs
Dung DinhSbornik: Mathematics 214 (4) 479 (2023)
https://doi.org/10.4213/sm9791e
Deep Learning in High Dimension: Neural Network Expression Rates for Analytic Functions in \(\pmb{L^2(\mathbb{R}^d,\gamma_d)}\)
Christoph Schwab and Jakob ZechSIAM/ASA Journal on Uncertainty Quantification 11 (1) 199 (2023)
https://doi.org/10.1137/21M1462738
Wavenumber-Explicit Parametric Holomorphy of Helmholtz Solutions in the Context of Uncertainty Quantification
E. A. Spence and J. WunschSIAM/ASA Journal on Uncertainty Quantification 11 (2) 567 (2023)
https://doi.org/10.1137/22M1486170
On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion
Martin Eigel, Oliver G. Ernst, Björn Sprungk and Lorenzo TamelliniSIAM Journal on Numerical Analysis 60 (2) 659 (2022)
https://doi.org/10.1137/20M1364722
Exponential ReLU DNN Expression of Holomorphic Maps in High Dimension
J. A. A. Opschoor, Ch. Schwab and J. ZechConstructive Approximation 55 (1) 537 (2022)
https://doi.org/10.1007/s00365-021-09542-5
Constructive Deep ReLU Neural Network Approximation
Lukas Herrmann, Joost A. A. Opschoor and Christoph SchwabJournal of Scientific Computing 90 (2) (2022)
https://doi.org/10.1007/s10915-021-01718-2
Sparse Approximation of Triangular Transports, Part I: The Finite-Dimensional Case
Jakob Zech and Youssef MarzoukConstructive Approximation 55 (3) 919 (2022)
https://doi.org/10.1007/s00365-022-09569-2
Sparse Approximation of Triangular Transports, Part II: The Infinite-Dimensional Case
Jakob Zech and Youssef MarzoukConstructive Approximation 55 (3) 987 (2022)
https://doi.org/10.1007/s00365-022-09570-9
Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs
Dinh DũngESAIM: Mathematical Modelling and Numerical Analysis 55 (3) 1163 (2021)
https://doi.org/10.1051/m2an/2021017
Higher-Order Quasi-Monte Carlo Training of Deep Neural Networks
Marcello Longo, Siddhartha Mishra, T. Konstantin Rusch and Christoph SchwabSIAM Journal on Scientific Computing 43 (6) A3938 (2021)
https://doi.org/10.1137/20M1369373