142 citations · 696 across the 46 of their papers we have counts for
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Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations
Holger Rauhut, Christoph Schwab
We analyze the convergence of compressive sensing based sampling techniques for the efficient evaluation of functionals of solutions for a class of high-dimensional, affine-paramet…
Higher Order Quasi Monte-Carlo Integration in Uncertainty Quantification
Josef Dick, Quoc Thong Le Gia, Christoph Schwab
We review recent results on dimension-robust higher order convergence rates of Quasi-Monte Carlo Petrov-Galerkin approximations for response functionals of infinite-dimensional, pa…
Efficient Resolution of Anisotropic Structures
Wolfgang Dahmen, Chunyan Huang, Gitta Kutyniok +3
We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in…
Higher order Quasi-Monte Carlo integration for holomorphic, parametric operator equations
Josef Dick, Quoc T. Le Gia, Christoph Schwab
We analyze the convergence of higher order Quasi-Monte Carlo (QMC) quadratures of solution-functionals to countably-parametric, nonlinear operator equations with distributed uncert…
Multi-level higher order QMC Galerkin discretization for affine parametric operator equations
Josef Dick, Frances Kuo, Quoc Thong Le Gia +1
We develop a convergence analysis of a multi-level algorithm combining higher order quasi-Monte Carlo (QMC) quadratures with general Petrov-Galerkin discretizations of countably af…