Sparse adaptive approximation of high dimensional parametric initial value problems

DOI10.1007/s10013-013-0011-9zbMath1272.34012OpenAlexW2000408025MaRDI QIDQ353046

Markus Hansen, Christoph Schwab

Publication date: 12 July 2013

Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11850/154965

zbMATH Keywords

ordinary differential equationsinitial value problemTaylor series\(N\)-term approximationanalyticity in infinite-dimensional spacesparametric dependence

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Nonlinear differential equations in abstract spaces (34G20) Infinite-dimensional holomorphy (46G20) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)

Related Items

Sparse-grid, reduced-basis Bayesian inversion, QMC Galerkin Discretization of Parametric Operator Equations, Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients, Scaling limits in computational Bayesian inversion, Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations, Optimal approximation of infinite-dimensional holomorphic functions, Posterior consistency for Gaussian process approximations of Bayesian posterior distributions, Higher order quasi-Monte Carlo integration for Bayesian PDE inversion, On the Complexity of Parametric ODEs and Related Problems, Multilevel higher-order quasi-Monte Carlo Bayesian estimation, Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs, Complexity of parametric initial value problems in Banach spaces, Adaptive Sparse Grid Model Order Reduction for Fast Bayesian Estimation and Inversion, A mixed ℓ₁ regularization approach for sparse simultaneous approximation of parameterized PDEs, Multilevel Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations, Multilevel approximation of parametric and stochastic PDES, Higher Order Quasi Monte-Carlo Integration in Uncertainty Quantification, Higher-Order Quasi-Monte Carlo Training of Deep Neural Networks, The Vlasov-Fokker-Planck equation with high dimensional parametric forcing term

Uses Software

• RODAS

Cites Work

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