A literature survey of low-rank tensor approximation techniques

DOI10.1002/gamm.201310004zbMath1279.65045arXiv1302.7121OpenAlexW1967077133MaRDI QIDQ2864808

Daniel Kressner, Lars Grasedyck, Christine Tobler

Publication date: 26 November 2013

Published in: GAMM-Mitteilungen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.7121

zbMATH Keywords

tensor linear systems eigenvalue problems multivariate functions low rank

Mathematics Subject Classification ID

Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).

Related Items (only showing first 100 items - show all)

Tensor Regression Using Low-Rank and Sparse Tucker Decompositions ⋮ Randomized Algorithms for Rounding in the Tensor-Train Format ⋮ Rank Bounds for Approximating Gaussian Densities in the Tensor-Train Format ⋮ On Fully Real Eigenconfigurations of Tensors ⋮ A Least-Squares Method for Sparse Low Rank Approximation of Multivariate Functions ⋮ Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format ⋮ Low-Rank Eigenvector Compression of Posterior Covariance Matrices for Linear Gaussian Inverse Problems ⋮ Tensor-based dynamic mode decomposition ⋮ Tensor Completion in Hierarchical Tensor Representations ⋮ Computational Methods for Linear Matrix Equations ⋮ SOTT: Greedy Approximation of a Tensor as a Sum of Tensor Trains ⋮ A nonlinearly preconditioned conjugate gradient algorithm for rank‐R canonical tensor approximation ⋮ Tensor-based multiscale method for diffusion problems in quasi-periodic heterogeneous media ⋮ Solving coupled tensor equations via higher order LSQR methods ⋮ Fast computation of the multidimensional fractional Laplacian ⋮ Performance of the Low-Rank TT-SVD for Large Dense Tensors on Modern MultiCore CPUs ⋮ Tensor Approximation of Stationary Distributions of Chemical Reaction Networks ⋮ Simultaneous state-time approximation of the chemical master equation using tensor product formats ⋮ Cubature, Approximation, and Isotropy in the Hypercube ⋮ Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations ⋮ Low-rank tensor structure preservation in fractional operators by means of exponential sums ⋮ Algebraic compressed sensing ⋮ Low-rank tensor methods for partial differential equations ⋮ Perturbation of Higher-Order Singular Values ⋮ Data-Driven Tensor Train Gradient Cross Approximation for Hamilton–Jacobi–Bellman Equations ⋮ Full-rank and low-rank splitting methods for the Swift-Hohenberg equation ⋮ Randomized algorithms for the computation of multilinear rank-\((\mu_1,\mu_2,\mu_3)\) approximations ⋮ On the rate of polynomial approximations of holomorphic functions on convex compact sets ⋮ A literature survey of matrix methods for data science ⋮ Detection thresholds in very sparse matrix completion ⋮ Streaming Tensor Train Approximation ⋮ Constrained Optimization with Low-Rank Tensors and Applications to Parametric Problems with PDEs ⋮ TTDFT: a GPU accelerated Tucker tensor DFT code for large-scale Kohn-Sham DFT calculations ⋮ Parallel Algorithms for Computing the Tensor-Train Decomposition ⋮ Minimality of tensors of fixed multilinear rank ⋮ A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations ⋮ Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system ⋮ A Novel Variable-Separation Method Based on Sparse and Low Rank Representation for Stochastic Partial Differential Equations ⋮ Hybrid Kronecker Product Decomposition and Approximation ⋮ Low Rank Symmetric Tensor Approximations ⋮ Structure-Preserving Low Multilinear Rank Approximation of Antisymmetric Tensors ⋮ Chebfun in Three Dimensions ⋮ Data-driven reduced order models using invariant foliations, manifolds and autoencoders ⋮ Low-Rank Tensor Approximations for Solving Multimarginal Optimal Transport Problems ⋮ A low-rank isogeometric solver based on Tucker tensors ⋮ Low-Rank Solution to an Optimization Problem Constrained by the Navier--Stokes Equations ⋮ An Efficient Block Rational Krylov Solver for Sylvester Equations with Adaptive Pole Selection ⋮ Literature survey on low rank approximation of matrices ⋮ Stochastic Methods for Solving High-Dimensional Partial Differential Equations ⋮ Using the Tensor-Train Approach to Solve the Ground-State Eigenproblem for Hydrogen Molecules ⋮ Numerical methods for the deterministic second moment equation of parabolic stochastic PDEs ⋮ An Adaptive Stochastic Galerkin Tensor Train Discretization for Randomly Perturbed Domains ⋮ Hankel Tensor Decompositions and Ranks ⋮ Low-Rank Tensor Approximation for Chebyshev Interpolation in Parametric Option Pricing ⋮ Exploiting Efficient Representations in Large-Scale Tensor Decompositions ⋮ Geometric Methods on Low-Rank Matrix and Tensor Manifolds ⋮ Tensor Train Construction From Tensor Actions, With Application to Compression of Large High Order Derivative Tensors ⋮ Adaptive Hierarchical Subtensor Partitioning for Tensor Compression ⋮ Range-Separated Tensor Format for Many-Particle Modeling ⋮ Jacobi--Davidson Method on Low-Rank Matrix Manifolds ⋮ Norm and Trace Estimation with Random Rank-one Vectors ⋮ Low-Rank Tensor Recovery using Sequentially Optimal Modal Projections in Iterative Hard Thresholding (SeMPIHT) ⋮ Fast tensor method for summation of long‐range potentials on 3D lattices with defects ⋮ Preconditioned Low-rank Riemannian Optimization for Linear Systems with Tensor Product Structure ⋮ Reduced Basis Methods: From Low-Rank Matrices to Low-Rank Tensors ⋮ Tensor numerical methods for multidimensional PDES: theoretical analysis and initial applications ⋮ Numerical tensor calculus ⋮ Tensor Algorithms for Advanced Sensitivity Metrics ⋮ Real‐time iterative learning control‐two applications with time scales between years and nanoseconds ⋮ Randomized Alternating Least Squares for Canonical Tensor Decompositions: Application to A PDE With Random Data ⋮ HOID: Higher Order Interpolatory Decomposition for Tensors Based on Tucker Representation ⋮ A TT-Based Hierarchical Framework for Decomposing High-Order Tensors ⋮ Analysis of Parametric Models for Coupled Systems ⋮ Adaptive low-rank methods for problems on Sobolev spaces with error control in L₂ ⋮ Riemannian Optimization for High-Dimensional Tensor Completion ⋮ A Geometric Description of Feasible Singular Values in the Tensor Train Format ⋮ Numerical algorithms for high-performance computational science ⋮ Preconditioners and Tensor Product Solvers for Optimal Control Problems from Chemotaxis ⋮ Adaptive low-rank approximations for operator equations: Accuracy control and computational complexity ⋮ A Semi-Lagrangian Vlasov Solver in Tensor Train Format ⋮ The impact of competition between cancer cells and healthy cells on optimal drug delivery ⋮ Fast Multidimensional Convolution in Low-Rank Tensor Formats via Cross Approximation ⋮ A Higher Order Unscented Transform ⋮ Unnamed Item ⋮ Robust Alternating Direction Implicit Solver in Quantized Tensor Formats for a Three-Dimensional Elliptic PDE ⋮ On the Compressibility of Tensors ⋮ Tensor Spaces and Hierarchical Tensor Representations ⋮ Bayesian inversion for electromyography using low-rank tensor formats ⋮ Optimal Local Approximation Spaces for Parabolic Problems ⋮ Tensor Manifold with Tucker Rank Constraints ⋮ Estimating a Few Extreme Singular Values and Vectors for Large-Scale Matrices in Tensor Train Format ⋮ Randomized Algorithms for Low-Rank Tensor Decompositions in the Tucker Format ⋮ ISLET: Fast and Optimal Low-Rank Tensor Regression via Importance Sketching ⋮ Tensor decomposition and high-performance computing for solving high-dimensional stochastic control system numerically ⋮ Convergence rate analysis for the higher order power method in best rank one approximations of tensors ⋮ Numerical solution of high dimensional stationary Fokker-Planck equations via tensor decomposition and Chebyshev spectral differentiation ⋮ Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion ⋮ Solving systems of polynomial equations -- a tensor approach ⋮ Uncertainty propagation in orbital mechanics via tensor decomposition ⋮ Sum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids

Uses Software

Cites Work

This page was built for publication: A literature survey of low-rank tensor approximation techniques