Projection methods for dynamical low-rank approximation of high-dimensional problems

DOI10.1515/cmam-2018-0029zbMath1448.65064OpenAlexW2884158030MaRDI QIDQ2324352

Bart Vandereycken, Emil Kieri

Publication date: 11 September 2019

Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/cmam-2018-0029

zbMATH Keywords

error estimatesprojection methodslow-rank approximationtensor traintensor differential equations

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for low-rank matrix approximation; matrix compression (65F55)

Related Items (14)

A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds ⋮ Adaptive integration of nonlinear evolution equations on tensor manifolds ⋮ Dynamically Orthogonal Runge–Kutta Schemes with Perturbative Retractions for the Dynamical Low-Rank Approximation ⋮ Low-rank tensor methods for partial differential equations ⋮ Implicit integration of nonlinear evolution equations on tensor manifolds ⋮ Tensor rank reduction via coordinate flows ⋮ A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations ⋮ Low-rank parareal: a low-rank parallel-in-time integrator ⋮ Stable Rank-Adaptive Dynamically Orthogonal Runge–Kutta Schemes ⋮ Geometric Methods on Low-Rank Matrix and Tensor Manifolds ⋮ Time Integration of Rank-Constrained Tucker Tensors ⋮ Rank-adaptive tensor methods for high-dimensional nonlinear PDEs ⋮ Stability properties of a projector-splitting scheme for dynamical low rank approximation of random parabolic equations ⋮ Editorial. Tensor numerical methods: actual theory and recent applications

Uses Software

• MCTDH
• TensorToolbox.jl

Cites Work

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