DOI10.1137/140953289zbMath1307.65035arXiv1304.1222OpenAlexW1996869553MaRDI QIDQ2940008
Dmitry V. Savostyanov, Sergey V. Dolgov
Publication date: 23 January 2015
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1301.6068
QTT-isogeometric solver in two dimensions,
Rank-Adaptive Time Integration of Tree Tensor Networks,
Randomized Algorithms for Rounding in the Tensor-Train Format,
Adaptive stochastic Galerkin FEM with hierarchical tensor representations,
Matrix-equation-based strategies for convection-diffusion equations,
Numerical approximation of Poisson problems in long domains,
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,
Solving phase-field models in the tensor train format to generate microstructures of bicontinuous composites,
Computation of extreme eigenvalues in higher dimensions using block tensor train format,
Truncated low‐rank methods for solving general linear matrix equations,
Enhanced alternating energy minimization methods for stochastic Galerkin matrix equations,
Alternating Linear Scheme in a Bayesian Framework for Low-Rank Tensor Approximation,
QTT-finite-element approximation for multiscale problems. I: Model problems in one dimension,
Solving coupled tensor equations via higher order LSQR methods,
Iterative methods based on soft thresholding of hierarchical tensors,
A low-rank solver for the stochastic unsteady Navier-Stokes problem,
Computing Low-Rank Approximations of Large-Scale Matrices with the Tensor Network Randomized SVD,
Low-rank solvers for unsteady Stokes-Brinkman optimal control problem with random data,
Low-rank tensor structure preservation in fractional operators by means of exponential sums,
Low-rank tensor methods for partial differential equations,
Data-Driven Tensor Train Gradient Cross Approximation for Hamilton–Jacobi–Bellman Equations,
Constrained Optimization with Low-Rank Tensors and Applications to Parametric Problems with PDEs,
Fast preconditioned iterative methods for fractional Sturm–Liouville equations,
Tensor product approach to modelling epidemics on networks,
Parallel Algorithms for Computing the Tensor-Train Decomposition,
Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions,
Study of performance of low-rank nonnegative tensor factorization methods,
Stochastic Evaluation of Large Interdependent Composed Models Through Kronecker Algebra and Exponential Sums,
A two-step accelerated Levenberg-Marquardt method for solving multilinear systems in tensor-train format,
Scalable conditional deep inverse Rosenblatt transports using tensor trains and gradient-based dimension reduction,
Deep Importance Sampling Using Tensor Trains with Application to a Priori and a Posteriori Rare Events,
Low-Rank Solution to an Optimization Problem Constrained by the Navier--Stokes Equations,
Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs,
HT-AWGM: a hierarchical Tucker-adaptive wavelet Galerkin method for high-dimensional elliptic problems,
Low-rank Riemannian eigensolver for high-dimensional Hamiltonians,
Tensor Product Approach to Quantum Control,
Tensorisation in the Solution of Smoluchowski Type Equations,
Sampling-free Bayesian inversion with adaptive hierarchical tensor representations,
Geometric Methods on Low-Rank Matrix and Tensor Manifolds,
Fast tensor product solvers for optimization problems with fractional differential equations as constraints,
Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations,
Multigrid methods combined with low-rank approximation for tensor-structured Markov chains,
Direct tensor-product solution of one-dimensional elliptic equations with parameter-dependent coefficients,
Block tensor train decomposition for missing data estimation,
Greedy low-rank approximation in Tucker format of solutions of tensor linear systems,
Preconditioned Low-rank Riemannian Optimization for Linear Systems with Tensor Product Structure,
Reduced Basis Methods: From Low-Rank Matrices to Low-Rank Tensors,
Block structured preconditioners in tensor form for the all-at-once solution of a finite volume fractional diffusion equation,
Multigrid Methods for Tensor Structured Markov Chains with Low Rank Approximation,
Fast low-rank solution of the multidimensional hyperbolic problems,
Tensor Algorithms for Advanced Sensitivity Metrics,
Matrix equation techniques for certain evolutionary partial differential equations,
Adaptive Low-Rank Methods: Problems on Sobolev Spaces,
A Low-Rank Tensor Method for PDE-Constrained Optimization with Isogeometric Analysis,
Regularized Computation of Approximate Pseudoinverse of Large Matrices Using Low-Rank Tensor Train Decompositions,
Computing functions of very large matrices with small TT/QTT ranks by quadrature formulas,
Approximation and sampling of multivariate probability distributions in the tensor train decomposition,
Parallel ALS Algorithm for Solving Linear Systems in the Hierarchical Tucker Representation,
Adaptive low-rank methods for problems on Sobolev spaces with error control in L2,
Low-rank tensor approximation of singularly perturbed boundary value problems in one dimension,
Solving differential Riccati equations: a nonlinear space-time method using tensor trains,
A Hybrid Alternating Least Squares--TT-Cross Algorithm for Parametric PDEs,
Riemannian Optimization for High-Dimensional Tensor Completion,
A tensor decomposition algorithm for large ODEs with conservation laws,
Approximate solution of linear systems with Laplace-like operators via cross approximation in the frequency domain,
Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations,
Adaptive low-rank approximations for operator equations: Accuracy control and computational complexity,
Fundamental tensor operations for large-scale data analysis using tensor network formats,
A Semi-Lagrangian Vlasov Solver in Tensor Train Format,
Tensor representation of non-linear models using cross approximations,
Stable als approximation in the TT-format for rank-adaptive tensor completion,
Fast Multidimensional Convolution in Low-Rank Tensor Formats via Cross Approximation,
Computing Eigenspaces With Low Rank Constraints,
Robust Alternating Direction Implicit Solver in Quantized Tensor Formats for a Three-Dimensional Elliptic PDE,
Tensor train based isogeometric analysis for PDE approximation on parameter dependent geometries,
Deep composition of tensor-trains using squared inverse Rosenblatt transports,
Tensor Bi-CR Methods for Solutions of High Order Tensor Equation Accompanied by Einstein Product,
Corrected One-Site Density Matrix Renormalization Group and Alternating Minimal Energy Algorithm,
Estimating a Few Extreme Singular Values and Vectors for Large-Scale Matrices in Tensor Train Format,
Hand-waving and interpretive dance: an introductory course on tensor networks