Algorithm 941: htucker - A Matlab Toolbox for Tensors in Hierarchical Tucker Format

By Daniel Kressner, Christine Tobler. 2014

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “The htucker toolbox [173] provides a M ATLAB class representing a tensor in HT decomposition.”
On the approximation of high-dimensional differential equations in the hierarchical Tucker format (2013, methodology): “This idea has ﬁrst been used in quantum chemistry to solve high-dimensional Schrödinger equations [13, 15, 16] and later been investigated from a mathematical point of view in [2, 4, 12, 14]; see also [10] for a useful M ATLAB toolbox.”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, methodology): “…Tucker toolbox by Kressner and Tobler (http://www. sam.math.ethz.ch/NLAgroup/htucker_toolbox.html) focuses mostly on HT type of tensor networks [Kressner and Tobler, 2014], which avoid explicit computation of the SVDs when truncating a tensor which is already in a HT format [Espig et al.,…”
Low-rank tensor methods for linear systems and eigenvalue problems (2012, background): “Most contents of this chapter are based on [50].”
Multilevel preconditioning and low‐rank tensor iteration for space–time simultaneous discretizations of parabolic PDEs (2015, methodology): “The following numerical experiments are based on the publicly available htucker toolbox [41, 42] in MATLAB, which provides a representation of a tensor in the H-Tucker format, as well as the operations described earlier.”
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].”
Algorithm 941 (2014, background): “Examples for working with htucker and a list of its complete functionality can be found in the preprint [Kressner and Tobler 2012], an extended version of this manuscript.”
Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors (2013, methodology): “Throughout this section, we define n := maxτ∈L{nτ} and denote the maximal hierarchical rank of X by kX , and when Z is in HT format the analogue by kZ In the implementation, we make heavy use of the tensor toolbox [2] and the htucker toolbox [19].”