Dynamical low-rank approximation: Applications and numerical experiments

DOI10.1016/j.matcom.2008.03.007zbMath1162.65335OpenAlexW2049887960MaRDI QIDQ1010057

Christian Lubich, Achim Nonnenmacher

Publication date: 3 April 2009

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2008.03.007

zbMATH Keywords

numerical exampleimage compressioninformation retrievalblow-updifferential equationsmodel reductionreaction-diffusion equationlatent semantic indexingtensor approximationdynamical low-rank approximation

Mathematics Subject Classification ID

Related Items (28)

A low-rank method for two-dimensional time-dependent radiation transport calculations ⋮ Dynamic tensor approximation of high-dimensional nonlinear PDEs ⋮ A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds ⋮ A mass, momentum, and energy conservative dynamical low-rank scheme for the Vlasov equation ⋮ A high-order/low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations ⋮ A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations ⋮ A dynamical low-rank approach to the chemical master equation ⋮ Numerical low-rank approximation of matrix differential equations ⋮ The geometry of algorithms using hierarchical tensors ⋮ Dynamical low-rank approximation to the solution of parabolic differential equations ⋮ Convergence Results for Projected Line-Search Methods on Varieties of Low-Rank Matrices Via Łojasiewicz Inequality ⋮ Accelerating the simulation of kinetic shear Alfvén waves with a dynamical low-rank approximation ⋮ Recompression of Hadamard Products of Tensors in Tucker Format ⋮ Locating coalescing singular values of large two-parameter matrices ⋮ An optimization approach for dynamical Tucker tensor approximation ⋮ Geometric multiscale decompositions of dynamic low-rank matrices ⋮ A projector-splitting integrator for dynamical low-rank approximation ⋮ A Low-Rank Algorithm for Weakly Compressible Flow ⋮ A Low-Rank Projector-Splitting Integrator for the Vlasov--Poisson Equation ⋮ Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values ⋮ Rank-adaptive tensor methods for high-dimensional nonlinear PDEs ⋮ Convergence of a Low-Rank Lie--Trotter Splitting for Stiff Matrix Differential Equations ⋮ A Quasi-Conservative Dynamical Low-Rank Algorithm for the Vlasov Equation ⋮ Projection methods for dynamical low-rank approximation of high-dimensional problems ⋮ Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit ⋮ A literature survey of low-rank tensor approximation techniques ⋮ Continuous Decompositions and Coalescing Eigenvalues for Matrices Depending on Parameters ⋮ A sweep-based low-rank method for the discrete ordinate transport equation

Uses Software

• RODAS
• TensorToolbox
• Algorithm 862
• MCTDH

Cites Work

• A dynamical low-rank approach to the chemical master equation
• Algorithm 862
• On Smooth Decompositions of Matrices
• Matrices, Vector Spaces, and Information Retrieval
• A Multilinear Singular Value Decomposition
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• On variational approximations in quantum molecular dynamics
• On Updating Problems in Latent Semantic Indexing
• Using Linear Algebra for Intelligent Information Retrieval
• Dynamical Low‐Rank Approximation
• Geometric Numerical Integration

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