On the approximation of high-dimensional differential equations in the hierarchical Tucker format

DOI10.1007/s10543-013-0444-2zbMath1308.65113OpenAlexW2002633056MaRDI QIDQ398615

Tobias Jahnke, Andreas Arnold

Publication date: 15 August 2014

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://publikationen.bibliothek.kit.edu/1000029523/2254404

zbMATH Keywords

error boundstensor approximationDirac-Frenkel variational principlehierarchical Tucker formathigh-dimensional differential equations

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Multilinear algebra, tensor calculus (15A69) Numerical linear algebra (65F99)

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Uses Software

• htucker

Cites Work

• Tensor Decompositions and Applications
• The geometry of algorithms using hierarchical tensors
• From quantum to classical molecular dynamics: Reduced models and numerical analysis.
• A new scheme for the tensor representation
• On manifolds of tensors of fixed TT-rank
• Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors
• Hierarchical Singular Value Decomposition of Tensors
• Dynamical Tensor Approximation
• Tensor Spaces and Numerical Tensor Calculus
• Matrix Analysis
• A Multilinear Singular Value Decomposition
• Algorithm 941
• Dynamical Low‐Rank Approximation