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TensorToolbox

swMATH ID: 4185
Software Authors: Bader, Brett W.; Kolda, Tamara G.
Description: Efficient MATLAB computations with sparse and factored tensors. The term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: A Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.
Homepage: http://www.sandia.gov/~tgkolda/TensorToolbox/index-2.5.html
Dependencies: Matlab
Keywords: sparse multidimensional arrays; multilinear algebraic computations; tensor decompositions; Tucker model; parallel factors (PARAFAC) model; MATLAB classes; canonical decomposition (CANDECOMP)
Related Software: Algorithm 862; Matlab; Tensorlab; TT Toolbox; N-way Toolbox; SPLATT; htucker; GitHub; DFacTo; GigaTensor; Poblano; TenEig; RandNLA; Anderson; Chebfun; BCLS; Multilinear Engine; TensorLy; mctoolbox; LSQR
Cited in: 186 Publications
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Cited by 348 Authors

9 Kolda, Tamara Gibson
8 Kressner, Daniel
8 Wei, Yimin
7 De Sterck, Hans
7 Qi, Liqun
6 Ma, Changfeng
5 Beik, Fatemeh Panjeh Ali
5 Che, Maolin
5 He, Hongjin
5 Huang, Baohua
5 Ling, Chen
4 Benner, Peter
4 Chen, Zhen
4 Han, Lixing
4 Lu, Linzhang
4 Najafi-Kalyani, Mehdi
4 Oseledets, Ivan V.
4 Saberi Movahed, Farid
3 Ballard, Grey M.
3 Chen, Chiyu
3 Chen, Yannan
3 Eldén, Lars
3 Feng, Lihong
3 Guan, Hongbo
3 Heyouni, Mohammed
3 Li, Donghui
3 Lubich, Christian
3 Tajaddini, Azita
3 Tobler, Christine
3 Tyrtyshnikov, Evgeniĭ Evgen’evich
3 Yan, Hong
3 Zhang, Liping
3 Zhou, Guanglu
2 Bader, Brett W.
2 Bai, Xueli
2 Balaji, Bhashyam
2 Banagaaya, Nicodemus
2 Ceruti, Gianluca
2 Chen, Bilian
2 Cichocki, Andrzej
2 De Lathauwer, Lieven
2 Demiralp, Metin
2 Dreesen, Philippe
2 Elbouyahyaoui, Lakhdar
2 Exl, Lukas
2 Fan, Hung-Yuan
2 Ge, Zhili
2 Hackbusch, Wolfgang
2 Hajarian, Masoud
2 Hong, David
2 Ishteva, Mariya
2 Jbilou, Khalide
2 Karimi, Saeed
2 Kaya, Oguz
2 Ke, Yifen
2 Khosravi Dehdezi, Eisa
2 Li, Zhening
2 Liang, Maolin
2 Ng, Michael Kwok-Po
2 Ni, Qin
2 Özay, Evrim Korkmaz
2 Reichel, Lothar
2 Savas, Berkant
2 Song, Yisheng
2 Uschmajew, André
2 Wang, Qingwen
2 Weiland, Siep
2 Xu, Xiangjian
2 Xu, Yangyang
2 Xu, Yi
2 Yang, Yuning
2 Yu, Gaohang
2 Yu, Zefeng
2 Zeng, Chao
2 Zhang, Shuzhong
2 Zhang, Xin
2 Zhao, Ruijuan
2 Zheng, Bing
1 Abdallah, Emad E.
1 Abdou, Joanna E.
1 Aditya, Konduri
1 Ahmadi-Asl, Salman
1 Ahmed, Talal
1 Ahn, Jeongyoun
1 Ammar, Amine
1 Anandkumar, Animashree
1 Anisimov, Anatoly V.
1 Auzinger, Winfried
1 Bai, Minru
1 Bajwa, Waheed Uz Zaman
1 Bance, S.
1 Barnard, Richard C.
1 Batselier, Kim
1 Battaglino, Casey
1 Bebendorf, Mario
1 Becker, Stephen R.
1 Ben Hamza, Abdessamad
1 Benson, Austin R.
1 Beylkin, Daniel
1 Beylkin, Gregory
...and 248 more Authors
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Cited in 75 Serials

17 SIAM Journal on Scientific Computing
12 Journal of Computational and Applied Mathematics
12 SIAM Journal on Matrix Analysis and Applications
7 Applied Mathematics and Computation
7 Numerical Algorithms
7 Linear Algebra and its Applications
6 Applied Numerical Mathematics
6 Journal of Scientific Computing
6 Numerical Linear Algebra with Applications
4 Computer Methods in Applied Mechanics and Engineering
4 Journal of Computational Physics
4 Computational Optimization and Applications
4 Science China. Mathematics
3 Linear and Multilinear Algebra
3 ACM Transactions on Mathematical Software
3 Journal of Optimization Theory and Applications
3 Numerische Mathematik
3 Computational and Applied Mathematics
3 Journal of Mathematical Chemistry
3 Journal of Machine Learning Research (JMLR)
3 SIAM Journal on Mathematics of Data Science
2 BIT
2 Calcolo
2 Applied Mathematics Letters
2 Journal of Global Optimization
2 SIAM Review
2 SIAM Journal on Optimization
2 Journal of Statistical Mechanics: Theory and Experiment
2 Statistical Analysis and Data Mining
2 SIAM Journal on Applied Algebra and Geometry
1 Computers & Mathematics with Applications
1 Journal of the Franklin Institute
1 Mathematics of Computation
1 Information Sciences
1 International Journal for Numerical Methods in Engineering
1 Mathematics and Computers in Simulation
1 Numerical Functional Analysis and Optimization
1 SIAM Journal on Control and Optimization
1 SIAM Journal on Numerical Analysis
1 Journal of Symbolic Computation
1 Algorithmica
1 Multidimensional Systems and Signal Processing
1 Neural Computation
1 Applications of Mathematics
1 Pattern Recognition
1 Mathematical Programming. Series A. Series B
1 Cybernetics and Systems Analysis
1 Filomat
1 Advances in Computational Mathematics
1 Mathematical Problems in Engineering
1 Optimization Methods & Software
1 Data Mining and Knowledge Discovery
1 New Journal of Physics
1 Computational Geosciences
1 Lobachevskii Journal of Mathematics
1 International Game Theory Review
1 Scandinavian Actuarial Journal
1 Computational Methods in Applied Mathematics
1 Entropy
1 Quantum Information Processing
1 GAMM-Mitteilungen
1 Frontiers of Mathematics in China
1 Signal, Image and Video Processing
1 Quantum Information & Computation
1 SIAM Journal on Financial Mathematics
1 Mathematical Programming Computation
1 Journal of Computational and Graphical Statistics
1 Asian Journal of Control
1 Numerical Algebra, Control and Optimization
1 Journal of Applied Analysis and Computation
1 Journal of the Operations Research Society of China
1 JSIAM Letters
1 Journal of Mathematical Modeling
1 SN Operations Research Forum
1 Results in Applied Mathematics

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