Dynamical low-rank approximation: applications and numerical experiments

63 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Initially proposed for low-rank matrix manifolds in [166], dynamical low-rank methods have been extended to low-rank tensors in Tucker [167, 199], TT/MPS [118, 123, 163, 186], and HT [9, 186, 255] decomposition.”
Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors (2013, unknown): “, kd) in [15, 24] and [16], respectively.”
A Dynamical Low-Rank Approach to the Chemical Master Equation (2008, background): “[23, 32] for the two- and three-dimensional case): Proof of Theorem 1.”
The geometry of algorithms using hierarchical tensors (2013, unknown): “In addition to theoretical bounds on the approximation quality, the authors show in the numerical experiments that this continuous-time updating compares favorably to point-wise approximations like ALS; see also [39, 40] for applications.”
Dynamical Tensor Approximation (2010, methodology): “In other examples that we computed, this gain is larger when the size of the core tensor is smaller as compared to the original tensor size or when Ȧ is significantly sparser than A, as has similarly been observed in the dynamical low-rank approximation of large data matrices [15].”
A projector-splitting integrator for dynamical low-rank approximation (2013, methodology): “For large time-dependent matrices, this approach was proposed and analyzed in [6], and first numerical applications were given in [13].”