Hierarchical Singular Value Decomposition of Tensors
SIAM Journal on Matrix Analysis and Applications
Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
SIAM Journal on Matrix Analysis and Applications
AICT'11 Proceedings of the 2nd international conference on Applied informatics and computing theory
Array flattening based univariate high dimensional model representation (AFBUHDMR)
AICT'11 Proceedings of the 2nd international conference on Applied informatics and computing theory
Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs
SIAM Journal on Scientific Computing
Algebraic Wavelet Transform via Quantics Tensor Train Decomposition
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
A tensor decomposition approach to data compression and approximation of ND systems
Multidimensional Systems and Signal Processing
Classifying high-dimensional patterns using a fuzzy logic discriminant network
Advances in Fuzzy Systems - Special issue on Hybrid Biomedical Intelligent Systems
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
Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats
Computers & Mathematics with Applications
Journal of Computational Physics
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For $d$-dimensional tensors with possibly large $d3$, an hierarchical data structure, called the Tree-Tucker format, is presented as an alternative to the canonical decomposition. It has asymptotically the same (and often even smaller) number of representation parameters and viable stability properties. The approach involves a recursive construction described by a tree with the leafs corresponding to the Tucker decompositions of three-dimensional tensors, and is based on a sequence of SVDs for the recursively obtained unfolding matrices and on the auxiliary dimensions added to the initial “spatial” dimensions. It is shown how this format can be applied to the problem of multidimensional convolution. Convincing numerical examples are given.