Black box approximation of tensors in hierarchical Tucker format

By Jonas Ballani, Lars Grasedyck, Melanie Kluge. 2013

183 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mathematics

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Also based on ﬁber crosses, a black box approximation for a tensor in the HT decomposition is given in [14,17].”
Algorithm 941 (2014, methodology): “2013] and low-rank tensor cross-approximation for HTD [Ballani 2012; Ballani et al. 2012].”
Multilevel preconditioning and low‐rank tensor iteration for space–time simultaneous discretizations of parabolic PDEs (2015, methodology): “In the following numerical experiment, we use a MATLAB implementation [48] of the algorithm described in [43, 44].”
Low-rank methods for high-dimensional approximation and model order reduction (2015, unknown): “structured set of entries selected adaptively. Algorithms have also been proposed for an adaptive construction of low-rank approximations of ain Tensor Train format [72] or Hierarchical Tucker format [4]. These algorithms are extensions of Adaptive Cross Approximation (ACA) algorithm to high-order t”
Tensor Ring Decomposition (2016, background): “Another important tensor network is the hierarchical Tucker (HT) format [33], [34], in which a recursive, hierarchical construction of Tucker type is employed for low-dimensional representation.”
Tensors for Data Mining and Data Fusion (2016, methodology): “The ﬁrst way is the so-called Hierarchical Tucker Decomposition (H-Tucker) [Hackbusch and K¨uhn 2009; Grasedyck 2010; Kressner and Tobler 2012; Ballani et al. 2013].”
Fast adaptive interpolation of multi-dimensional arrays in tensor train format (2011, methodology): “Recently, for the H-Tucker format [26], [27], an adaptive black-box version based on the successive cross approximation of subtensors was presented by Ballani, Grasedyck and Kluge, with good examples of efficiency [28].”
Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis (2014, background): “Examples of tensor networks are the hierarchical Tucker (HT) decompositions and Tensor Trains (TT) (see Figure 9) [15], [16].”
Fast evaluation of singular BEM integrals based on tensor approximations (2012, methodology): “We could further generalise these results to the H-Tucker format in [1].”
On Local Convergence of Alternating Schemes for Optimization of Convex Problems in the Tensor Train Format (2013, background): “[1, 2, 22, 26, 29]; while the former approach seems to be superior on some problems in the sense that it sometimes provides lower ranks [16], the latter has advantage of being conceptually quite simple, thus often allowing for a simpler analysis from the theoretical point of view, and enabling, from”