Low-rank tensor structure of linear diffusion operators in the TT and QTT formats
DOI10.1016/j.laa.2013.01.009zbMath1281.15024OpenAlexW1973615963MaRDI QIDQ389698
Oleg Reichmann, Christoph Schwab, Vladimir A. Kazeev
Publication date: 21 January 2014
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2013.01.009
curse of dimensionalitysemiseparable matriceslow-rank representationdiffusion operatorquasi-separable matricestensor train (TT) and quantized tensor train (QTT) formats
Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Multilinear algebra, tensor calculus (15A69) Numerical linear algebra (65F99)
Related Items (21)
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Cites Work
- Unnamed Item
- Tensor Decompositions and Applications
- Tensor-Train Decomposition
- On Kolmogorov equations for anisotropic multivariate Lévy processes
- \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling
- Approximation of matrices with logarithmic number of parameters
- Linear complexity algorithms for semiseparable matrices
- On a new class of structured matrices
- The strong Kronecker product
- Constructive representation of functions in low-rank tensor formats
- A new scheme for the tensor representation
- Two-Level QTT-Tucker Format for Optimized Tensor Calculus
- The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
- Hierarchical Singular Value Decomposition of Tensors
- Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
- QTT approximation of elliptic solution operators in higher dimensions
- EXISTENCE AND EQUILIBRATION OF GLOBAL WEAK SOLUTIONS TO KINETIC MODELS FOR DILUTE POLYMERS I: FINITELY EXTENSIBLE NONLINEAR BEAD-SPRING CHAINS
- Numerical Solution of the Hartree–Fock Equation in Multilevel Tensor-Structured Format
- Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs
- Tensor Spaces and Numerical Tensor Calculus
- Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
- Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems
- Tensor approximations of matrices generated by asymptotically smooth functions
- Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse
- Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker--Planck Equation
- A projection method to solve linear systems in tensor format
- Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems
- Efficient Hierarchical Approximation of High‐Dimensional Option Pricing Problems
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