Adaptive Low-Rank Methods: Problems on Sobolev Spaces

DOI10.1137/140978223zbMath1336.41009arXiv1407.4919OpenAlexW2181385834MaRDI QIDQ2796861

Wolfgang Dahmen, Markus Bachmayr

Publication date: 30 March 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.4919

zbMATH Keywords

computational complexitypreconditioningadaptive methodslow-rank tensor approximationhigh-dimensional elliptic problems

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Multidimensional problems (41A63) Numerical solutions to equations with linear operators (65J10) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46) Numerical approximation and computational geometry (primarily algorithms) (65D99)

Related Items (14)

Singular value decomposition in Sobolev spaces. II ⋮ Iterative methods based on soft thresholding of hierarchical tensors ⋮ Low-rank tensor methods for partial differential equations ⋮ State estimation in nonlinear parametric time dependent systems using tensor train ⋮ Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions ⋮ Pricing High-Dimensional Bermudan Options with Hierarchical Tensor Formats ⋮ A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations ⋮ Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs ⋮ HT-AWGM: a hierarchical Tucker-adaptive wavelet Galerkin method for high-dimensional elliptic problems ⋮ Partial tensor decomposition for decoupling isogeometric Galerkin discretizations ⋮ Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations ⋮ Adaptive low-rank methods for problems on Sobolev spaces with error control in L₂ ⋮ Existence of dynamical low-rank approximations to parabolic problems ⋮ Adaptive low-rank approximations for operator equations: Accuracy control and computational complexity

Uses Software

• LOBPCG

Cites Work

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