Dynamical Low-Rank Approximation

By Othmar Koch, Christian Lubich. 2007

405 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

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In Applied Mathematics

In Computational Mechanics

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Citations in the corpus

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.”
A Dynamical Low-Rank Approach to the Chemical Master Equation (2008, background): “1 of [23]: Since the ODE is linear, the bounds (6.”
A projector-splitting integrator for dynamical low-rank approximation (2013, methodology): “4 of [6] yields, since S′′ = O(δ) and (S′)−1 = O(1), K21 = B21 ( S′ )− + O(δ)”
The geometry of algorithms using hierarchical tensors (2013, methodology): “3] and [48] have appeared that also extend the dynamical low-rank algorithm from [37, 38] to HT tensors using the same tangent space and choice of gauge as ours.”
Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors (2013, methodology): “The proofs are the same as for the corresponding results in [15] and [16], using Lemma 4.”
Tensor-product approach to global time-space-parametric discretization of chemical master equation (2012, background): “For a detailed description we refer to [20, 21, 22].”
Low-Rank Matrix Completion by Riemannian Optimization (2012, background): “, [25, 29] for applications of gradient flows on Mk), more advanced concepts like retraction-based optimization onMk have only very recently been investigated; see [47, 48].”
Dynamical low-rank approximation: applications and numerical experiments (2008, methodology): “comparison with the best low-rank approximation, are studied in [ 12 ].”
Dynamical Tensor Approximation (2010, background): “While we have kept the general organisation of the paper largely parallel to [8] to make similarities and differences easily visible, we note that the material in §2 is quite apart from the matrix case in both notation and techniques, and the analysis of the tangent space projection in §3 requires d”
Efficient time-stepping scheme for dynamics on TT-manifolds (2012, positive): “1 Equations of motion in the general case In this section a general framework for the dynamical low-rank approximation in the TTformat will be derived, following the ideas of [20, 19, 22].”
On manifolds of tensors of fixed TT-rank (2012, methodology): “To illustrate the range of applications, we now review a well-known ansatz [20, 26, 33] for how partial differential equations and optimisation problems posed in high-dimensional spaces Rn1×.”