On Smooth Decompositions of Matrices
SIAM Journal on Matrix Analysis and Applications
On Updating Problems in Latent Semantic Indexing
SIAM Journal on Scientific Computing
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
Algorithm 862: MATLAB tensor classes for fast algorithm prototyping
ACM Transactions on Mathematical Software (TOMS)
Dynamical Low-Rank Approximation
SIAM Journal on Matrix Analysis and Applications
Locating coalescing singular values of large two-parameter matrices
Mathematics and Computers in Simulation
Dynamical Tensor Approximation
SIAM Journal on Matrix Analysis and Applications
Geometric multiscale decompositions of dynamic low-rank matrices
Computer Aided Geometric Design
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Dynamical low-rank approximation is a differential-equation-based approach to efficiently compute low-rank approximations to time-dependent large data matrices or to solutions of large matrix differential equations. We illustrate its use in the following application areas: as an updating procedure in latent semantic indexing for information retrieval, in the compression of series of images, and in the solution of time-dependent partial differential equations, specifically on a blow-up problem of a reaction-diffusion equation in two and three spatial dimensions. In 3D and higher dimensions, space discretization yields a tensor differential equation whose solution is approximated by low-rank tensors, effectively solving a system of discretized partial differential equations in one spatial dimension.