Parallel Algorithms for Computing the Tensor-Train Decomposition
From MaRDI portal
Publication:6097870
DOI10.1137/21m146079xzbMath1517.65032arXiv2111.10448MaRDI QIDQ6097870
Unnamed Author, Tianyi Shi, Alex Townsend
Publication date: 7 June 2023
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2111.10448
Parallel numerical computation (65Y05) Multilinear algebra, tensor calculus (15A69) Numerical methods for low-rank matrix approximation; matrix compression (65F55)
Related Items (3)
Generative modeling via tensor train sketching ⋮ Streaming Tensor Train Approximation ⋮ High-dimensional density estimation with tensorizing flow
Cites Work
- Unnamed Item
- Unnamed Item
- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- Tensor Decompositions and Applications
- Tensor-Train Decomposition
- TT-cross approximation for multidimensional arrays
- Rang revealing QR factorizations
- On the ADI method for Sylvester equations
- On the singular values of matrices with high displacement rank
- Dimensionality reduction in higher-order signal processing and rank-\((R_1,R_2,\ldots,R_N)\) reduction in multilinear algebra
- Randomized algorithms for the approximations of Tucker and the tensor train decompositions
- MERACLE: constructive layer-wise conversion of a tensor train into a MERA
- Two-Level QTT-Tucker Format for Optimized Tensor Calculus
- A literature survey of low-rank tensor approximation techniques
- Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions
- 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
- Tensor Spaces and Numerical Tensor Calculus
- Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
- Computational Methods for Linear Matrix Equations
- A Multilinear Singular Value Decomposition
- Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker--Planck Equation
- TT-GMRES: solution to a linear system in the structured tensor format
- Parallel Algorithms for Tensor Train Arithmetic
- Low-Rank Tucker Approximation of a Tensor from Streaming Data
- Parallel Algorithms for Low Rank Tensor Arithmetic
- TuckerMPI
- Adaptive Hierarchical Subtensor Partitioning for Tensor Compression
- Fast Poisson solvers for spectral methods
- On the Compressibility of Tensors
- Randomized Algorithms for Rounding in the Tensor-Train Format
This page was built for publication: Parallel Algorithms for Computing the Tensor-Train Decomposition
