Numerical tensor calculus (Q4683918)

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scientific article; zbMATH DE number 6944161

Language	Label	Description	Also known as
English	Numerical tensor calculus	scientific article; zbMATH DE number 6944161

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scholarly article

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Numerical tensor calculus (English)

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zbMATH Open document ID

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10.1017/S0962492914000087

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publication date

26 September 2018

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Mathematics Subject Classification ID

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zbMATH DE Number

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Wolfgang Hackbusch

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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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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Adaptive cross approximation of multivariate functions

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Low rank methods for a class of generalized Lyapunov equations and related issues

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Algorithms for Numerical Analysis in High Dimensions

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Approximation by exponential sums revisited

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Approximating a wavefunction as an unconstrained sum of Slater determinants

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Approximate Solutions for the Bilinear Form Computational Problem

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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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On the third secant variety

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On Generic Identifiability of 3-Tensors of Small Rank

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Decompositions of a Higher-Order Tensor in Block Terms—Part II: Definitions and Uniqueness

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A Multilinear Singular Value Decomposition

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On the Best Rank-1 and Rank-(<i>R</i><sub>1</sub> ,<i>R</i><sub>2</sub> ,. . .,<i>R<sub>N</sub></i>) Approximation of Higher-Order Tensors

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

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Superfast Fourier transform using QTT approximation

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

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Black box low tensor-rank approximation using fiber-crosses

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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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Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces

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Best<i>N</i>-term approximation in electronic structure calculations I. One-electron reduced density matrix

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Best<i>N</i>-term approximation in electronic structure calculations. II. Jastrow factors

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\(\mathcal H\)-matrix approximation for the operator exponential with applications

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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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A literature survey of low-rank tensor approximation techniques

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Iterative solution of large sparse systems of equations. Transl. from the German

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Hierarchische Matrizen

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Tensorisation of vectors and their efficient convolution

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Tensor Spaces and Numerical Tensor Calculus

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\(L^{\infty}\) estimation of tensor truncations

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Tensor-product approximation to operators and functions in high dimensions

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A new scheme for the tensor representation

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Hierarchical Kronecker tensor-product approximations

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Approximate iterations for structured matrices

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Tensor rank is NP-complete

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Functions of Matrices

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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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Global properties of tensor rank

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Computations in quantum tensor networks

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

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

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Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs

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

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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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Applied Multiway Data Analysis

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Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics

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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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A center-of-mass principle for the multiparticle Schrödinger equation

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Musings on multilinear fitting

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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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Tensor-Train Decomposition

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

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Linear algebra for tensor problems

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Cross approximation in tensor electron density computations

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Tensor-train ranks for matrices and their inverses

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Krylov-type methods for tensor computations.I

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Fast truncation of mode ranks for bilinear tensor operations

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Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs

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Canonical Polyadic Decomposition with a Columnwise Orthonormal Factor Matrix

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On Uniqueness of the <i>n</i>th Order Tensor Decomposition into Rank-1 Terms with Linear Independence in One Mode

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Gaussian elimination is not optimal

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Well-posedness of convex maximization problems on Stiefel manifolds and orthogonal tensor product approximations

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

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On multiplication of 2 \(\times\) 2 matrices

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Regularity and approximability of electronic wave functions

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full work available at URL

https://doi.org/10.1017/s0962492914000087

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mardi Publication:4683918

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