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 74 articles )

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  1. Che, Maolin; Wei, Yimin; Yan, Hong: The computation of low multilinear rank approximations of tensors via power scheme and random projection (2020)
  2. Glau, Kathrin; Kressner, Daniel; Statti, Francesco: Low-rank tensor approximation for Chebyshev interpolation in parametric option pricing (2020)
  3. Hong, David; Kolda, Tamara G.; Duersch, Jed A.: Generalized canonical polyadic tensor decomposition (2020)
  4. Kumar, K. Harish; Jiwari, Ram: Legendre wavelets based numerical algorithm for simulation of multidimensional Benjamin-Bona-Mahony-Burgers and Sobolev equations (2020)
  5. Liu, Dongdong; Li, Wen; Vong, Seak-Weng: A new preconditioned SOR method for solving multi-linear systems with an (\mathcalM)-tensor (2020)
  6. Malik, Osman Asif; Becker, Stephen: Guarantees for the Kronecker fast Johnson-Lindenstrauss transform using a coherence and sampling argument (2020)
  7. Benson, Austin R.; Gleich, David F.: Computing tensor (Z)-eigenvectors with dynamical systems (2019)
  8. Bentkamp, Alexander; Blanchette, Jasmin Christian; Klakow, Dietrich: A formal proof of the expressiveness of deep learning (2019)
  9. Chen, Yannan; Sun, Wenyu; Xi, Min; Yuan, Jinyun: A seminorm regularized alternating least squares algorithm for canonical tensor decomposition (2019)
  10. Chou, Lot-Kei; Lei, Siu-Long: Tensor-train format solution with preconditioned iterative method for high dimensional time-dependent space-fractional diffusion equations with error analysis (2019)
  11. Gao, David: Canonical duality-triality theory: unified understanding for modeling, problems, and NP-hardness in global optimization of multi-scale systems (2019)
  12. Hnětynková, Iveta; Plešinger, Martin; Žáková, Jana: On TLS formulation and core reduction for data fitting with generalized models (2019)
  13. Li, Zhibao; Dai, Yu-Hong; Gao, Huan: Alternating projection method for a class of tensor equations (2019)
  14. Phipps, Eric T.; Kolda, Tamara G.: Software for sparse tensor decomposition on emerging computing architectures (2019)
  15. Battaglino, Casey; Ballard, Grey; Kolda, Tamara G.: A practical randomized CP tensor decomposition (2018)
  16. Eustaquio, Rodrigo G.; Ribeiro, Ademir A.; Dumett, Miguel A.: A new class of root-finding methods in (\mathbbR^n): the inexact tensor-free Chebyshev-Halley class (2018)
  17. Guan, Yu; Chu, Moody T.; Chu, Delin: Convergence analysis of an SVD-based algorithm for the best rank-1 tensor approximation (2018)
  18. Gu, Chuanqing; Liu, Yong: The tensor Padé-type approximant with application in computing tensor exponential function (2018)
  19. Harrison, A. P.; Joseph, D.: High performance rearrangement and multiplication routines for sparse tensor arithmetic (2018)
  20. Kepner, Jeremy; Jananthan, Hayden: Mathematics of big data. Spreadsheets, databases, matrices, and graphs. With a foreword by Charles E. Leiserson (2018)

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