Efficient time-stepping scheme for dynamics on TT-manifolds

By Boris N. Khoromskij, Ivan V. Oseledets, Reinhold Schneider. 2012

30 citations recorded by the source corpus.

Citations in the corpus

• ALTERNATING MINIMAL ENERGY METHODS FOR LINEAR SYSTEMS IN HIGHER DIMENSIONS∗ (2014, unknown): “The KSL scheme is efficient in simulation of molecular vibrations [46].”
• Low-Rank Tensor Learning with Discriminant Analysis for Action Classification and Image Recovery (2014, unknown): “…representation learning approaches have been proposed (Chen and Saad 2009; Koch and Lubich 2010; Haegeman et al. 2011; Holtz, Rohwedder, and Schneider 2012; Khoromskij, Oseledets , and Schneider 2012; Arnold and Jahnke 2012; Lubich et al. 2013; Uschmajew and Vandereycken 2013; Mu et al. 2013).”
• Tensor-product approach to global time-space-parametric discretization of chemical master equation (2012, unknown): “For a detailed description we refer to [20, 21, 22].”
• Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors (2013, unknown): “, [6, 14] for approaches to other time-dependent equations using TT.”
• Geometric Methods on Low-Rank Matrix and Tensor Manifolds (2020, unknown): “A very reasonable way to do this is the following [56, 103].”
• Low-rank tensor structure of linear diffusion operators in the TT and QTT formats☆ (2013, unknown): “The computational efficiency of the TT, QTT and Hierarchical Tensor [19, 20] representations has been demonstrated in many papers, including [21, 22, 23] on elliptic PDEs and eigenvalue problems, [24, 25, 26] on parabolic PDEs, [27] on nonlinear EVPs, [28] on multi-parametric problems, [29] on stoch”
• Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, unknown): “The KSL scheme is efficient in simulation of molecular vibrations [46].”
• Approximation rates for the hierarchical tensor format in periodic Sobolev spaces (2014, unknown): “in [23], and for Fokker Planck equation in [11].”