TKPSVD swMATH ID: 28028 Software Authors: Batselier, Kim; Wong, Ngai Description: A constructive arbitrary-degree Kronecker product decomposition of tensors. We propose the tensor Kronecker product singular value decomposition (TKPSVD) that decomposes a real k-way tensor A into a linear combination of tensor Kronecker products with an arbitrary number of d factors A=∑Rj=1σjA(d)j⊗⋯⊗A(1)j. We generalize the matrix Kronecker product to tensors such that each factor A(i)j in the TKPSVD is a k-way tensor. The algorithm relies on reshaping and permuting the original tensor into a d-way tensor, after which a polyadic decomposition with orthogonal rank-1 terms is computed. We prove that for many different structured tensors, the Kronecker product factors A(1)j,…,A(d)j are guaranteed to inherit this structure. In addition, we introduce the new notion of general symmetric tensors, which includes many different structures such as symmetric, persymmetric, centrosymmetric, Toeplitz and Hankel tensors. Homepage: https://arxiv.org/pdf/1507.08805.pdf Source Code: https://github.com/kbatseli/TKPSVD Dependencies: Matlab Keywords: generalized symmetric tensors; Hankel tensor; Kronecker product; structured tensors; tensor decomposition; Toeplitz tensor Related Software: Tensorlab; Matlab; TensorToolbox; GQTPAR; LAPACK; Algorithm 862 Cited in: 13 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A constructive arbitrary-degree Kronecker product decomposition of tensors. Zbl 1424.15045Batselier, Kim; Wong, Ngai 2017 all top 5 Cited by 24 Authors 5 Batselier, Kim 1 Boralevi, Ada 1 Che, Maolin 1 Chen, Zhongming 1 Chu, Delin 1 Chu, Moody T. 1 Cichocki, Andrzej 1 Draisma, Jan 1 Ehrlacher, Virginie 1 Fan, Jinyan 1 Fu, Taoran 1 Guan, Yu 1 Horobeţ, Emil 1 Hu, ShengLong 1 Jin, Xiaoqing 1 Koiran, Pascal 1 Liu, Haotian 1 Liu, Weihui 1 Lombardi, Damiano 1 Robeva, Elina 1 Ruiz, Maria Fuente 1 Wang, Xuezhong 1 Wei, Yimin 1 Xie, Ze-Jia all top 5 Cited in 11 Serials 2 Journal of Computational and Applied Mathematics 2 SIAM Journal on Matrix Analysis and Applications 1 Israel Journal of Mathematics 1 Linear and Multilinear Algebra 1 Automatica 1 Computational Optimization and Applications 1 SIAM Journal on Scientific Computing 1 Numerical Linear Algebra with Applications 1 Journal of the Operations Research Society of China 1 East Asian Journal on Applied Mathematics 1 Communications on Applied Mathematics and Computation Cited in 5 Fields 12 Linear and multilinear algebra; matrix theory (15-XX) 9 Numerical analysis (65-XX) 2 Operations research, mathematical programming (90-XX) 2 Systems theory; control (93-XX) 1 Differential geometry (53-XX) Citations by Year