A literature survey of low-rank tensor approximation techniques (Q2864808)

scientific article; zbMATH DE number 6232884

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English	A literature survey of low-rank tensor approximation techniques	scientific article; zbMATH DE number 6232884

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instance of

scholarly article

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title

A literature survey of low-rank tensor approximation techniques (English)

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26 November 2013

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full work available at URL

https://arxiv.org/abs/1302.7121

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zbMATH Keywords

tensor

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low rank

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multivariate functions

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linear systems

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eigenvalue problems

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describes a project that uses

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On the convergence of a greedy rank-one update algorithm for a class of linear systems

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A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids

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A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids. II: Transient simulation using space-time separated representations

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Non incremental strategies based on separated representations: applications in computational rheology

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Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

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Algorithm 862

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Fast evaluation of singular BEM integrals based on tensor approximations

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A projection method to solve linear systems in tensor format

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Black box approximation of tensors in hierarchical Tucker format

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Approximation of boundary element matrices

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Adaptive cross approximation of multivariate functions

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Adaptive low-rank approximation of collocation matrices

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Low-rank quadrature-based tensor approximation of the Galerkin projected Newton/Yukawa kernels

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Multivariate Regression and Machine Learning with Sums of Separable Functions

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Numerical operator calculus in higher dimensions

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Algorithms for Numerical Analysis in High Dimensions

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On approximation of functions by exponential sums

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Approximation by exponential sums revisited

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Approximation of the electron density of aluminium clusters in tensor-product format

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Progress in industrial mathematics at ECMI 2010. Proceedings of the 16th European conference on mathematics for industry, Wuppertal, Germany, July 26--30, 2010

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Hybrid cross approximation of integral operators

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Approximation of 1/x by exponential sums in [1, ∞)

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On the efficient computation of high-dimensional integrals and the approximation by exponential sums

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CONVERGENCE OF A GREEDY ALGORITHM FOR HIGH-DIMENSIONAL CONVEX NONLINEAR PROBLEMS

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New ALS Methods With Extrapolating Search Directions and Optimal Step Size for Complex-Valued Tensor Decompositions

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Alleviating mesh constraints: model reduction, parallel time integration and high resolution homogenization

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Efficient multi-scale computation of products of orbitals in electronic structure calculations

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Convergence rates of best $N$-term Galerkin approximations for a class of elliptic SPDEs

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ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S

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Riemannian Optimization on Tensor Products of Grassmann Manifolds: Applications to Generalized Rayleigh-Quotients

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A Multilinear Singular Value Decomposition

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Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem

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A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition

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Superfast Fourier transform using QTT approximation

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Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker--Planck Equation

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Solution of Linear Systems and Matrix Inversion in the TT-Format

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A least-squares approximation of partial differential equations with high-dimensional random inputs

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A randomized algorithm for a tensor-based generalization of the singular value decomposition

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A Newton–Grassmann Method for Computing the Best Multilinear Rank-$(r_1,$ $r_2,$ $r_3)$ Approximation of a Tensor

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Black box low tensor-rank approximation using fiber-crosses

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A regularized Newton method for the efficient approximation of tensors represented in the canonical tensor format

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Optimization problems in contracted tensor networks

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Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats

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Variational calculus with sums of elementary tensors of fixed rank

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FFT-based Kronecker product approximation to micromagnetic long-range interactions

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Fast stray field computation on tensor grids

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On minimal subspaces in tensor representations

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A proper generalized decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach

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Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces

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Greedy approximation of high-dimensional Ornstein-Uhlenbeck operators

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Q3086662

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Verification of the cross 3D algorithm on quantum chemistry data

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Fast low rank approximations of matrices and tensors

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Tensor completion and low-n-rank tensor recovery via convex optimization

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Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems

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Quantized-TT-Cayley transform for computing the dynamics and the spectrum of high-dimensional Hamiltonians

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Tensor-based methods for numerical homogenization from high-resolution images

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Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case

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Q3086656

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A theory of pseudoskeleton approximations

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Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure

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Hierarchical Singular Value Decomposition of Tensors

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An introduction to hierarchical ($\mathcal H$-) rank and TT-rank of tensors with examples

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Tensorisation of vectors and their efficient convolution

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Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators I. Separable approximation of multi-variate functions

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Low-rank Kronecker-product approximation to multi-dimensional nonlocal operators II. HKT representation of certain operators

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Tensor-product approximation to operators and functions in high dimensions

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Tensor-Product Approximation to Multidimensional Integral Operators and Green's Functions

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Use of tensor formats in elliptic eigenvalue problems

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Hierarchical Kronecker tensor-product approximations

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Approximate iterations for structured matrices

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A new scheme for the tensor representation

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Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions

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On manifolds of tensors of fixed TT-rank

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The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format

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Computations in quantum tensor networks

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Exploiting matrix symmetries and physical symmetries in matrix product states and tensor trains

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Q3572292

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Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme

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Differential-geometric Newton method for the best rank-$(R _{1}, R _{2}, R _{3})$ approximation of tensors

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A dynamical low-rank approach to the chemical master equation

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Low-rank tensor structure of linear diffusion operators in the TT and QTT formats

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Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse

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Structure of the Hessian matrix and an economical implementation of Newton’s method in the problem of canonical approximation of tensors

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Computation of the Hartree-Fock exchange by the tensor-structured methods

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Black-Box Hartree–Fock Solver by Tensor Numerical Methods

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Fast and accurate 3D tensor calculation of the Fock operator in a general basis

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QTT representation of the Hartree and exchange operators in electronic structure calculations

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Tensor-Structured Factorized Calculation of Two-Electron Integrals in a General Basis

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Structured Rank-(r1, . . . , rd) Decomposition of Function-related Tensors in R_D

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Structured data-sparse approximation to high order tensors arising from the deterministic Boltzmann equation

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Tensor-structured preconditioners and approximate inverse of elliptic operators in $\mathbb R^{d}$

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Fast and accurate tensor approximation of a multivariate convolution with linear scaling in dimension

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$O(d \log N)$-quantics approximation of $N$-$d$ tensors in high-dimensional numerical modeling

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Low rank Tucker-type tensor approximation to classical potentials

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Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays

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Tensor decomposition in electronic structure calculations on 3D Cartesian grids

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Numerical Solution of the Hartree–Fock Equation in Multilevel Tensor-Structured Format

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Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs

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QTT approximation of elliptic solution operators in higher dimensions

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Fast quadrature techniques for retarded potentials based on TT/QTT tensor approximation

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Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs

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Dynamical Low‐Rank Approximation

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Dynamical Tensor Approximation

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Tensor Decompositions and Applications

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Krylov Subspace Methods for Linear Systems with Tensor Product Structure

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Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems

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Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems

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Algorithm 941

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Routes for efficient computational homogenization of~nonlinear materials using the~proper generalized decompositions

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Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations

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Block tensor conjugate gradient-type method for Rayleigh quotient minimization in two-dimensional case

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Tensor conjugate-gradient-type method for Rayleigh quotient minimization in block QTT-format

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On variational approximations in quantum molecular dynamics

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From quantum to classical molecular dynamics: Reduced models and numerical analysis.

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Dynamical approximation by hierarchical Tucker and tensor-train tensors

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Computing Inner Eigenvalues of Matrices in Tensor Train Matrix Format

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Solving stochastic systems with low-rank tensor compression

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Tensor structured evaluation of singular volume integrals

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Q5396620

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Musings on multilinear fitting

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Trigonometric identities and sums of separable functions

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A fully deterministic micro-macro simulation of complex flows involving reversible network fluid models

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Generalized cross approximation for 3D-tensors

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Dynamical low-rank approximation: Applications and numerical experiments

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A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations

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Generalized spectral decomposition method for solving stochastic finite element equations: invariant subspace problem and dedicated algorithms

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Proper generalized decompositions and separated representations for the numerical solution of high dimensional stochastic problems

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Tensor properties of multilevel Toeplitz and related matrices

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Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition

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DMRG approach to fast linear algebra in the TT-format

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Constructive representation of functions in low-rank tensor formats

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Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time

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Linear algebra for tensor problems

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Cross approximation in tensor electron density computations

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Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions

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TT-cross approximation for multidimensional arrays

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Algebraic Wavelet Transform via Quantics Tensor Train Decomposition

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Tensor-train ranks for matrices and their inverses

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Tensor-Train Decomposition

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Q3522633

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Low Complexity Damped Gauss--Newton Algorithms for CANDECOMP/PARAFAC

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Enhanced Line Search: A Novel Method to Accelerate PARAFAC

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On local convergence of alternating schemes for optimization of convex problems in the tensor train format

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Krylov-type methods for tensor computations.I

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Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors

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QTT-rank-one vectors with QTT-rank-one and full-rank Fourier images

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Fast truncation of mode ranks for bilinear tensor operations

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The density-matrix renormalization group in the age of matrix product states

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Computational Methods for Linear Matrix Equations

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Subtracting a best rank-1 approximation may increase tensor rank

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Algebraic reconstruction of the general-order poles of a meromorphic function

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Q3027578

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Estimates of best bilinear approximations of functions and approximation numbers of integral operators

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Incomplete cross approximation in the mosaic-skeleton method

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Tensor approximations of matrices generated by asymptotically smooth functions

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Kronecker-product approximations for some function-related matrices.

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A Kronecker Product Preconditioner for Stochastic Galerkin Finite Element Discretizations

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Regularity of tensor product approximations to square integrable functions

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Local Convergence of the Alternating Least Squares Algorithm for Canonical Tensor Approximation

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A Riemannian Optimization Approach for Computing Low-Rank Solutions of Lyapunov Equations

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A New Truncation Strategy for the Higher-Order Singular Value Decomposition

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Identifiers

zbMATH Open document ID

1279.65045

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Mathematics Subject Classification ID

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10.1002/GAMM.201310004

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Sitelinks

Mathematics(1 entry)

mardi Publication:2864808