Journal of Algorithms
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
Algorithms for Numerical Analysis in High Dimensions
SIAM Journal on Scientific Computing
Why Are High-Dimensional Finance Problems Often of Low Effective Dimension?
SIAM Journal on Scientific Computing
Pricing European multi-asset options using a space-time adaptive FD-method
Computing and Visualization in Science
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
SIAM Journal on Matrix Analysis and Applications
Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time
SIAM Journal on Matrix Analysis and Applications
Linear algebra for tensor problems
Computing
Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays
SIAM Journal on Scientific Computing
Tensor Decompositions and Applications
SIAM Review
Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
SIAM Journal on Scientific Computing
Hierarchical Singular Value Decomposition of Tensors
SIAM Journal on Matrix Analysis and Applications
Numerical Solution of the Hartree-Fock Equation in Multilevel Tensor-Structured Format
SIAM Journal on Scientific Computing
Algebraic Wavelet Transform via Quantics Tensor Train Decomposition
SIAM Journal on Scientific Computing
A New Truncation Strategy for the Higher-Order Singular Value Decomposition
SIAM Journal on Scientific Computing
The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
SIAM Journal on Scientific Computing
Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case
SIAM Journal on Scientific Computing
Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems
SIAM Journal on Matrix Analysis and Applications
An equi-directional generalization of adaptive cross approximation for higher-order tensors
Applied Numerical Mathematics
Superfast solution of linear convolutional Volterra equations using QTT approximation
Journal of Computational and Applied Mathematics
Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats
Computers & Mathematics with Applications
Approximation rates for the hierarchical tensor format in periodic Sobolev spaces
Journal of Complexity
Journal of Computational Physics
| Hi-index | 0.01 |
A simple nonrecursive form of the tensor decomposition in $d$ dimensions is presented. It does not inherently suffer from the curse of dimensionality, it has asymptotically the same number of parameters as the canonical decomposition, but it is stable and its computation is based on low-rank approximation of auxiliary unfolding matrices. The new form gives a clear and convenient way to implement all basic operations efficiently. A fast rounding procedure is presented, as well as basic linear algebra operations. Examples showing the benefits of the decomposition are given, and the efficiency is demonstrated by the computation of the smallest eigenvalue of a 19-dimensional operator.