Algorithm 862

Algorithm 862: MATLAB tensor classes for fast algorithm prototyping. Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB’s multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor_as_matrix class supports the “matricization” of a tensor, that is, the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp_tensor and tucker_tensor. We describe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 53 articles )

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  1. Battaglino, Casey; Ballard, Grey; Kolda, Tamara G.: A practical randomized CP tensor decomposition (2018)
  2. Guan, Yu; Chu, Moody T.; Chu, Delin: Convergence analysis of an SVD-based algorithm for the best rank-1 tensor approximation (2018)
  3. Gu, Chuanqing; Liu, Yong: The tensor Padé-type approximant with application in computing tensor exponential function (2018)
  4. Harrison, A. P.; Joseph, D.: High performance rearrangement and multiplication routines for sparse tensor arithmetic (2018)
  5. Khoromskaia, Venera; Khoromskij, Boris N.: Tensor numerical methods in quantum chemistry (2018)
  6. Matthews, Devin A.: High-performance tensor contraction without transposition (2018)
  7. Springer, Paul; Bientinesi, Paolo: Design of a high-performance GEMM-like tensor-tensor multiplication (2018)
  8. Xie, Ze-Jia; Cheng, Che-Man; Jin, Xiao-Qing: Some norm inequalities for commutators of contracted tensor products (2018)
  9. Zhu, Wei; Wang, Bao; Barnard, Richard; Hauck, Cory D.; Jenko, Frank; Osher, Stanley: Scientific data interpolation with low dimensional manifold model (2018)
  10. Cem Bassoy: TLib: A Flexible C++ Tensor Framework for Numerical Tensor Calculus (2017) arXiv
  11. De Sterck, Hans; Howse, Alexander: Nonlinearly preconditioned optimization on Grassmann manifolds for computing approximate Tucker tensor decompositions (2016)
  12. Etter, Simon: Parallel ALS algorithm for solving linear systems in the hierarchical Tucker representation (2016)
  13. Fan, H.-Y.; Zhang, L.; Chu, E. K.-w.; Wei, Y.: Q-less QR decomposition in inner product spaces (2016)
  14. Van Loan, Charles F.: Structured matrix problems from tensors (2016)
  15. Batselier, Kim; Liu, Haotian; Wong, Ngai: A constructive algorithm for decomposing a tensor into a finite sum of orthonormal rank-1 terms (2015)
  16. Kolda, Tamara G.: Numerical optimization for symmetric tensor decomposition (2015)
  17. Rockenfeller, Robert; Günther, Michael; Schmitt, Syn; Götz, Thomas: Comparative sensitivity analysis of muscle activation dynamics (2015)
  18. Ballico, Edoardo: On the typical rank of real polynomials (or symmetric tensors) with a fixed border rank (2014)
  19. Bebendorf, M.; Kuske, C.: Separation of variables for function generated high-order tensors (2014)
  20. Bhatt, Vineet; Kumar, S.: A CAS aided survey of CP decomposition and rank-1 approxition of a 3rd-order tensor (2014)

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