Algorithm 862 swMATH ID: 7347 Software Authors: Brett W. Bader; Tamara G. Kolda Description: 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. Homepage: http://dl.acm.org/citation.cfm?id=1186794 Dependencies: Matlab Related Software: TensorToolbox; Matlab; Tensorlab; htucker; TT Toolbox; N-way Toolbox; ERPWAVELAB; LAPACK; Blitz++; TAMRESH; POOMA; mctoolbox; TENSOLVE; RandNLA; Chebfun; Blendenpik; cross2D; DFacTo; SPLATT; GitHub Cited in: 81 Publications all top 5 Cited by 161 Authors 7 Kolda, Tamara Gibson 5 Wei, Yimin 4 Kressner, Daniel 3 Che, Maolin 3 Eldén, Lars 3 Savas, Berkant 2 Bader, Brett W. 2 Balaji, Bhashyam 2 Bentkamp, Alexander 2 Blanchette, Jasmin Christian 2 Chen, Yannan 2 Chou, Lot-Kei 2 Fan, Hung-Yuan 2 Jin, Xiaoqing 2 Klakow, Dietrich 2 Lei, Siulong 2 Li, Wen 2 Tobler, Christine 2 Xie, Ze-Jia 2 Yan, Hong 1 Auzinger, Winfried 1 Bahuguna, Sandeep-Kumar 1 Ballard, Grey M. 1 Ballico, Edoardo 1 Bance, S. 1 Barnard, Richard C. 1 Batselier, Kim 1 Battaglino, Casey 1 Bebendorf, Mario 1 Becker, Stephen R. 1 Behera, Ratikanta 1 Benson, Austin R. 1 Bhatt, Vineet 1 Bientinesi, Paolo 1 Bourennane, Salah 1 Bozorgmanesh, Hassan 1 Cai, Xingju 1 Chen, Guangliang 1 Chen, Jie 1 Chen, Juefei 1 Cheng, Cheman 1 Chu, Delin 1 Chu, Eric K.-W. 1 Chu, Moody T. 1 Comon, Pierre 1 Dai, Yu-Hong 1 De Lathauwer, Lieven 1 De Sterck, Hans 1 Deng, Mingyu 1 Döhler, Michael 1 Duersch, Jed A. 1 Dumett, Miguel A. 1 Dunlavy, Daniel M. 1 Etter, Simon 1 Eustaquio, Rodrigo G. 1 Exl, Lukas 1 Fossati, Caroline 1 Gao, David Yang 1 Gao, Huan 1 Ghannam, Mai 1 Glau, Kathrin 1 Gleich, David F. 1 Götz, Thomas B. 1 Grasedyck, Lars 1 Gu, Chuanqing 1 Guan, Yu 1 Gundersen, Geir 1 Günther, Michael 1 Guo, Xueping 1 Gusenbauer, Markus 1 Hajarian, Masoud 1 Han, Deren 1 Harrison, Andrew P. 1 Hauck, Cory D. 1 Hnětynková, Iveta 1 Hong, David 1 Howse, Alexander J. M. 1 Jananthan, Hayden 1 Jenko, Frank 1 Jiwari, Ram 1 Junkins, John L. 1 Karaman, Sertac 1 Kegelmeyer, W. Philip 1 Kepner, Jeremy 1 Khoromskaia, Venera 1 Khoromskiĭ, Boris Nikolaevich 1 Kilmer, Misha Elena 1 King-wah Chu, Eric 1 Kumar, K. Harish 1 Kunis, Stefan 1 Kuske, Christian 1 Leiserson, Charles E. 1 Lerman, Gilad 1 Li, Zhibao 1 Lim, Lek-Heng 1 Liţa, Lăcrămioara 1 Litvinenko, Alexander 1 Liu, Dongdong 1 Liu, Haotian 1 Liu, Weihui ...and 61 more Authors all top 5 Cited in 41 Serials 8 Linear Algebra and its Applications 8 SIAM Journal on Scientific Computing 7 SIAM Journal on Matrix Analysis and Applications 4 Journal of Scientific Computing 3 Computers & Mathematics with Applications 3 ACM Transactions on Mathematical Software 2 Journal of Computational Physics 2 Calcolo 2 Journal of Computational and Applied Mathematics 2 Applied Mathematical Modelling 2 Pattern Recognition 2 Computational and Applied Mathematics 2 Frontiers of Mathematics in China 2 Operators and Matrices 1 Linear and Multilinear Algebra 1 Acta Mathematica Vietnamica 1 Computing 1 Journal of Optimization Theory and Applications 1 Mathematics and Computers in Simulation 1 SIAM Journal on Numerical Analysis 1 Physica D 1 Journal of Automated Reasoning 1 Neural Networks 1 SIAM Review 1 Mathematical Programming. 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Series B 1 Numerical Linear Algebra with Applications 1 Nonlinear Dynamics 1 Optimization Methods & Software 1 Foundations of Computational Mathematics 1 Entropy 1 Journal of Statistical Mechanics: Theory and Experiment 1 GAMM-Mitteilungen 1 Computational & Mathematical Methods in Medicine 1 EURASIP Journal on Advances in Signal Processing 1 Electronic Journal of Statistics 1 SIAM Journal on Financial Mathematics 1 Journal of Computational and Graphical Statistics 1 Palestine Journal of Mathematics 1 East Asian Journal on Applied Mathematics 1 Journal of Function Spaces 1 MIT Lincoln Laboratory Series all top 5 Cited in 23 Fields 55 Linear and multilinear algebra; matrix theory (15-XX) 52 Numerical analysis (65-XX) 18 Computer science (68-XX) 7 Statistics (62-XX) 7 Operations research, mathematical programming (90-XX) 6 Partial differential equations (35-XX) 5 Information and communication theory, circuits (94-XX) 2 Algebraic geometry (14-XX) 2 Real functions (26-XX) 2 Approximations and expansions (41-XX) 2 Differential geometry (53-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) Citations by Year