Algorithm 941: htucker: htucker - A Matlab toolbox for tensors in hierarchical Tucker format. The hierarchical Tucker format is a storage-efficient scheme to approximate and represent tensors of possibly high order. This paper presents a Matlab toolbox, along with the underlying methodology and algorithms, which provides a convenient way to work with this format. The toolbox not only allows for the efficient storage and manipulation of tensors in hierarchical Tucker format but also others a set of tools for the development of higher-level algorithms. Several examples for the use of the toolbox are given.

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  1. Rörich, Anna; Werthmann, Tim A.; Göddeke, Dominik; Grasedyck, Lars: Bayesian inversion for electromyography using low-rank tensor formats (2021)
  2. Sutti, Marco; Vandereycken, Bart: Riemannian multigrid line search for low-rank problems (2021)
  3. Bachmayr, Markus; Kazeev, Vladimir: Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs (2020)
  4. Dektor, Alec; Venturi, Daniele: Dynamically orthogonal tensor methods for high-dimensional nonlinear PDEs (2020)
  5. Rodgers, Abram; Venturi, Daniele: Stability analysis of hierarchical tensor methods for time-dependent PDEs (2020)
  6. Zniyed, Yassine; Boyer, Rémy; de Almeida, André L. F.; Favier, Gérard: A TT-based hierarchical framework for decomposing high-order tensors (2020)
  7. Boelens, Arnout M. P.; Venturi, Daniele; Tartakovsky, Daniel M.: Parallel tensor methods for high-dimensional linear PDEs (2018)
  8. Venturi, Daniele: The numerical approximation of nonlinear functionals and functional differential equations (2018)
  9. Corveleyn, Samuel; Vandewalle, Stefan: Computation of the output of a function with fuzzy inputs based on a low-rank tensor approximation (2017)
  10. Fan, Hung-Yuan; Zhang, Liping; Chu, Eric King-wah; Wei, Yimin: Numerical solution to a linear equation with tensor product structure. (2017)
  11. Garreis, Sebastian; Ulbrich, Michael: Constrained optimization with low-rank tensors and applications to parametric problems with PDEs (2017)
  12. Hashemi, Behnam; Trefethen, Lloyd N.: Chebfun in three dimensions (2017)
  13. Kressner, Daniel; Periša, Lana: Recompression of Hadamard products of tensors in Tucker format (2017)
  14. Zhang, Junyu; Wen, Zaiwen; Zhang, Yin: Subspace methods with local refinements for eigenvalue computation using low-rank tensor-train format (2017)
  15. Beik, Fatemeh Panjeh Ali; Saberi Movahed, Farid; Ahmadi-Asl, Salman: On the Krylov subspace methods based on tensor format for positive definite Sylvester tensor equations. (2016)
  16. Bonizzoni, F.; Nobile, F.; Kressner, D.: Tensor train approximation of moment equations for elliptic equations with lognormal coefficient (2016)
  17. Fan, H.-Y.; Zhang, L.; Chu, E. K.-w.; Wei, Y.: Q-less QR decomposition in inner product spaces (2016)
  18. Kressner, Daniel; Steinlechner, Michael; Vandereycken, Bart: Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure (2016)
  19. Andreev, Roman; Tobler, Christine: Multilevel preconditioning and low-rank tensor iteration for space-time simultaneous discretizations of parabolic PDEs. (2015)
  20. Da Silva, Curt; Herrmann, Felix J.: Optimization on the hierarchical Tucker manifold - applications to tensor completion (2015)

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