Parallel Algorithms for Tensor Train Arithmetic

DOI10.1137/20M1387158zbMath1484.65088arXiv2011.06532OpenAlexW4210523970WikidataQ115214713 ScholiaQ115214713MaRDI QIDQ5028405

Hussam al Daas, Peter Benner, Grey Ballard

Publication date: 9 February 2022

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.06532

zbMATH Keywords

QRSVDparallel algorithmstensor trainlow-rank tensor format

Mathematics Subject Classification ID

Factorization of matrices (15A23) Parallel numerical computation (65Y05) Complexity and performance of numerical algorithms (65Y20) Multilinear algebra, tensor calculus (15A69) Numerical linear algebra (65F99)

Related Items (7)

Randomized Algorithms for Rounding in the Tensor-Train Format ⋮ Adaptive integration of nonlinear evolution equations on tensor manifolds ⋮ Performance of the Low-Rank TT-SVD for Large Dense Tensors on Modern MultiCore CPUs ⋮ Generative modeling via tensor train sketching ⋮ Implicit integration of nonlinear evolution equations on tensor manifolds ⋮ Tensor rank reduction via coordinate flows ⋮ Parallel Algorithms for Computing the Tensor-Train Decomposition

Uses Software

• Matlab
• PETSc
• Trilinos
• TensorToolbox
• TT Toolbox
• redbKIT
• Tensorlab
• GitHub
• TensorLy
• TuckerMPI
• SPLATT
• TensorToolbox.jl
• PLANC
• ADTT

Cites Work

• Tensor Decompositions and Applications
• Tensor-Train Decomposition
• TT-cross approximation for multidimensional arrays
• \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling
• Faster tensor train decomposition for sparse data
• A new scheme for the tensor representation
• Tensor train approximation of moment equations for elliptic equations with lognormal coefficient
• Low-rank solvers for unsteady Stokes-Brinkman optimal control problem with random data
• Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• Communication-optimal Parallel and Sequential QR and LU Factorizations
• Block Tensor Unfoldings
• Certified Reduced Basis Methods for Parametrized Partial Differential Equations
• Low-Rank Tensor Approximation for High-Order Correlation Functions of Gaussian Random Fields
• Low-Rank Solution to an Optimization Problem Constrained by the Navier--Stokes Equations
• Krylov Subspace Methods for Linear Systems with Tensor Product Structure
• An overview of the Trilinos project
• Numerical operator calculus in higher dimensions
• Tensor approximations of matrices generated by asymptotically smooth functions
• Communication lower bounds and optimal algorithms for numerical linear algebra
• PLANC
• TuckerMPI
• Recompression of Hadamard Products of Tensors in Tucker Format
• Reduced Basis Methods for Partial Differential Equations

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