Matrix analysis
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
Rank-One Approximation to High Order Tensors
SIAM Journal on Matrix Analysis and Applications
Beyond streams and graphs: dynamic tensor analysis
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Window-based Tensor Analysis on High-dimensional and Multi-aspect Streams
ICDM '06 Proceedings of the Sixth International Conference on Data Mining
Tensor-product approximation to operators and functions in high dimensions
Journal of Complexity
Dynamical Low-Rank Approximation
SIAM Journal on Matrix Analysis and Applications
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
SIAM Journal on Matrix Analysis and Applications
Dynamical low-rank approximation: applications and numerical experiments
Mathematics and Computers in Simulation
The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
SIAM Journal on Scientific Computing
Geometric multiscale decompositions of dynamic low-rank matrices
Computer Aided Geometric Design
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For the approximation of time-dependent data tensors and of solutions to tensor differential equations by tensors of low Tucker rank, we study a computational approach that can be viewed as a continuous-time updating procedure. This approach works with the increments rather than the full tensor and avoids the computation of decompositions of large matrices. In this method, the derivative is projected onto the tangent space of the manifold of tensors of Tucker rank $(r_1,\dots,r_N)$ at the current approximation. This yields nonlinear differential equations for the factors in a Tucker decomposition, suitable for numerical integration. Approximation properties of this approach are analyzed.