Optimization problems in contracted tensor networks

DOI10.1007/s00791-012-0183-yzbMath1380.49059OpenAlexW2048459485MaRDI QIDQ1695448

Mike Espig, Wolfgang Hackbusch, Stefan Handschuh, Reinhold Schneider

Publication date: 7 February 2018

Published in: Computing and Visualization in Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00791-012-0183-y

zbMATH Keywords

tensor representationtensor networktensor formatvariational calculus in tensor networks

Mathematics Subject Classification ID

Applications of graph theory (05C90) Vector and tensor algebra, theory of invariants (15A72) Miscellaneous topics in calculus of variations and optimal control (49N99)

Related Items (11)

Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats ⋮ MERACLE: constructive layer-wise conversion of a tensor train into a MERA ⋮ Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations ⋮ A note on tensor chain approximation ⋮ Algorithm 941 ⋮ Numerical tensor calculus ⋮ Hybrid tensor decomposition in neural network compression ⋮ Fundamental tensor operations for large-scale data analysis using tensor network formats ⋮ Tensor Spaces and Hierarchical Tensor Representations ⋮ A literature survey of low-rank tensor approximation techniques ⋮ Estimating a Few Extreme Singular Values and Vectors for Large-Scale Matrices in Tensor Train Format

Uses Software

• TensorCalculus

Cites Work

• Unnamed Item
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• Local Convergence of the Alternating Least Squares Algorithm for Canonical Tensor Approximation
• Hierarchical Singular Value Decomposition of Tensors
• Tensor Spaces and Numerical Tensor Calculus
• Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
• On the geometry of tensor network states
• Numerical operator calculus in higher dimensions
• Algorithms for Numerical Analysis in High Dimensions

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