Geometric Methods on Low-Rank Matrix and Tensor Manifolds (Q3300541)

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English	Geometric Methods on Low-Rank Matrix and Tensor Manifolds	scientific article

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scholarly article

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Geometric Methods on Low-Rank Matrix and Tensor Manifolds (English)

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André Uschmajew

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Bart Vandereycken

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Handbook of Variational Methods for Nonlinear Geometric Data

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publication date

29 July 2020

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/978-3-030-31351-7_9

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Low-rank retractions: a survey and new results

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Approximation of Large-Scale Dynamical Systems

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On the approximation of high-dimensional differential equations in the hierarchical Tucker format

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Adaptive near-optimal rank tensor approximation for high-dimensional operator equations

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Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations

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Parametric PDEs: sparse or low-rank approximations?

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A projection method to solve linear systems in tensor format

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Hierarchical Tensor Approximation of Output Quantities of Parameter-Dependent PDEs

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On optimality of approximate low rank solutions of large-scale matrix equations

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Global rates of convergence for nonconvex optimization on manifolds

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A Riemannian Trust Region Method for the Canonical Tensor Rank Approximation Problem

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The Power of Convex Relaxation: Near-Optimal Matrix Completion

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Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions

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Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives

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Tensor-sparsity of solutions to high-dimensional elliptic partial differential equations

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Numerical solution of the finite horizon stochastic linear quadratic control problem

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Positive definiteness in the numerical solution of Riccati differential equations

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Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions

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Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format

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Adaptive stochastic Galerkin FEM with hierarchical tensor representations

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A Low-Rank Algorithm for Weakly Compressible Flow

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A Low-Rank Projector-Splitting Integrator for the Vlasov--Poisson Equation

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A Quasi-Conservative Dynamical Low-Rank Algorithm for the Vlasov Equation

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

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A Geometric Approach to Dynamical Model Order Reduction

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Calculating the Singular Values and Pseudo-Inverse of a Matrix

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Hierarchical Singular Value Decomposition of Tensors

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A literature survey of low-rank tensor approximation techniques

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Nonsmooth trust region algorithms for locally Lipschitz functions on Riemannian manifolds

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Tensor Spaces and Numerical Tensor Calculus

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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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An area law for one-dimensional quantum systems

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Critical points of matrix least squares distance functions

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On manifolds of tensors of fixed TT-rank

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A Riemannian Gradient Sampling Algorithm for Nonsmooth Optimization on Manifolds

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Line Search Algorithms for Locally Lipschitz Functions on Riemannian Manifolds

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

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Tensor Numerical Methods in Quantum Chemistry

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

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Tensor numerical methods in scientific computing

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

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Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs

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Projection methods for dynamical low-rank approximation of high-dimensional problems

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Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values

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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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Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems

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Low-Rank Tensor Methods with Subspace Correction for Symmetric Eigenvalue Problems

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Low-rank tensor completion by Riemannian optimization

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Preconditioned Low-rank Riemannian Optimization for Linear Systems with Tensor Product Structure

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ARPACK Users' Guide

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Alternating Projections on Manifolds

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

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Time Integration in the Multiconfiguration Time-Dependent Hartree Method of Molecular Quantum Dynamics

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A projector-splitting integrator for dynamical low-rank approximation

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Time Integration of Tensor Trains

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Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors

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The Gradient Projection Method Along Geodesics

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An adaptive subdivision method for root finding of univariate polynomials

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Numerical low-rank approximation of matrix differential equations

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SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS

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Fixed-rank matrix factorizations and Riemannian low-rank optimization

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Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs

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

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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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TT-cross approximation for multidimensional arrays

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Convergence of a Low-Rank Lie--Trotter Splitting for Stiff Matrix Differential Equations

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Jacobi--Davidson Method on Low-Rank Matrix Manifolds

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Low-rank Riemannian eigensolver for high-dimensional Hamiltonians

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Low rank tensor recovery via iterative hard thresholding

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Dynamically orthogonal field equations for continuous stochastic dynamical systems

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Riemannian Stochastic Variance Reduced Gradient Algorithm with Retraction and Vector Transport

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

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Tensor Decomposition for Signal Processing and Machine Learning

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Learning with tensors: a framework based on convex optimization and spectral regularization

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Computational Methods for Linear Matrix Equations

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Riemannian Optimization for High-Dimensional Tensor Completion

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On the Early History of the Singular Value Decomposition

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Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients

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The geometry of algorithms using hierarchical tensors

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Low-Rank Matrix Completion by Riemannian Optimization

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

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Guarantees of Riemannian Optimization for Low Rank Matrix Recovery

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Identifiers

10.1007/978-3-030-31351-7_9

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:3300541

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