A literature survey of low-rank tensor approximation techniques

Abstract

During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey attempts to give a literature overview of current developments in this area, with an emphasis on function-related tensors.

References in corpus (5)

• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Valence Bond Solids for Quantum Computation
• Tensor operators: constructions and applications for long-range interaction systems
• Computations in Quantum Tensor Networks
• Exploiting Matrix Symmetries and Physical Symmetries in Matrix Product States and Tensor Trains

Cited by in corpus (30)

• Tensor product methods and entanglement optimization for ab initio quantum chemistry
• Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
• TensorLy: Tensor Learning in Python
• Multi-Layer Potfit: An Accurate Potential Representation for Efficient High-Dimensional Quantum Dynamics
• Tensor Numerical Methods in Quantum Chemistry: from Hartree-Fock Energy to Excited States
• A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems
• Quantum mechanics of open systems: Dissipaton theories
• Very Large-Scale Singular Value Decomposition Using Tensor Train Networks
• Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation
• Tensor Regression Using Low-rank and Sparse Tucker Decompositions
• Low-rank methods for high-dimensional approximation and model order reduction
• Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation
• A literature survey of matrix methods for data science
• Tensor Completion Algorithms in Big Data Analytics
• Efficient Visual Recognition with Deep Neural Networks: A Survey on Recent Advances and New Directions
• Convergence analysis of Riemannian Gauss-Newton methods and its connection with the geometric condition number
• Low-rank approximate inverse for preconditioning tensor-structured linear systems
• About Notations in Multiway Array Processing
• Range-separated tensor formats for numerical modeling of many-particle interaction potentials
• Tucker tensor method for fast grid-based summation of long-range potentials on 3D lattices with defects
• Hybrid Kronecker Product Decomposition and Approximation
• Tensor approximation of the self-diffusion matrix of tagged particle processes
• On the rank and the approximation of symmetric tensors
• A Ternary Non-Commutative Latent Factor Model for Scalable Three-Way Real Tensor Completion
• Reliability analysis of high-dimensional models using low-rank tensor approximations
• Computation of extremal eigenvalues of high-dimensional lattice-theoretic tensors via tensor-train decompositions
• Lower bound for the maximum of some derivative of Hardy's function
• Randomized Interpolative Decomposition of Separated Representations
• Nearly Low Rank Tensors and Their Approximations
• A N-Body Solver for Free Mesh Interpolation