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 86 articles )

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  1. Bozorgmanesh, Hassan; Hajarian, Masoud: Triangular decomposition of CP factors of a third-order tensor with application to solving nonlinear systems of equations (2022)
  2. Che, Maolin; Chen, Juefei; Wei, Yimin: Perturbations of the \textscTcurdecomposition for tensor valued data in the Tucker format (2022)
  3. Wen, Ya-qiong; Li, Wen: Riemannian conjugate gradient methods for computing the extreme eigenvalues of symmetric tensors (2022)
  4. Che, Maolin; Wei, Yimin; Yan, Hong: An efficient randomized algorithm for computing the approximate Tucker decomposition (2021)
  5. Chou, Lot-Kei; Lei, Siu-Long: Finite volume approximation with ADI scheme and low-rank solver for high dimensional spatial distributed-order fractional diffusion equations (2021)
  6. Liu, Wei-Hui; Xie, Ze-Jia; Jin, Xiao-Qing: Frobenius norm inequalities of commutators based on different products (2021)
  7. Behera, Ratikanta; Maji, Sandip; Mohapatra, R. N.: Weighted Moore-Penrose inverses of arbitrary-order tensors (2020)
  8. Che, Maolin; Wei, Yimin; Yan, Hong: The computation of low multilinear rank approximations of tensors via power scheme and random projection (2020)
  9. Deng, Ming-Yu; Guo, Xue-Ping: On HSS-based iteration methods for two classes of tensor equations (2020)
  10. Glau, Kathrin; Kressner, Daniel; Statti, Francesco: Low-rank tensor approximation for Chebyshev interpolation in parametric option pricing (2020)
  11. Hong, David; Kolda, Tamara G.; Duersch, Jed A.: Generalized canonical polyadic tensor decomposition (2020)
  12. Kumar, K. Harish; Jiwari, Ram: Legendre wavelets based numerical algorithm for simulation of multidimensional Benjamin-Bona-Mahony-Burgers and Sobolev equations (2020)
  13. Liu, Dongdong; Li, Wen; Vong, Seak-Weng: A new preconditioned SOR method for solving multi-linear systems with an (\mathcalM)-tensor (2020)
  14. Malik, Osman Asif; Becker, Stephen: Guarantees for the Kronecker fast Johnson-Lindenstrauss transform using a coherence and sampling argument (2020)
  15. Mickelin, Oscar; Karaman, Sertac: Multiresolution low-rank tensor formats (2020)
  16. Xie, Mengyan; Wang, Qing-Wen: Reducible solution to a quaternion tensor equation (2020)
  17. Benson, Austin R.; Gleich, David F.: Computing tensor (Z)-eigenvectors with dynamical systems (2019)
  18. Bentkamp, Alexander; Blanchette, Jasmin Christian; Klakow, Dietrich: A formal proof of the expressiveness of deep learning (2019)
  19. Chen, Yannan; Sun, Wenyu; Xi, Min; Yuan, Jinyun: A seminorm regularized alternating least squares algorithm for canonical tensor decomposition (2019)
  20. 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)

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