TKPSVD
swMATH ID:  28028 
Software Authors:  Batselier, Kim; Wong, Ngai 
Description:  A constructive arbitrarydegree Kronecker product decomposition of tensors. We propose the tensor Kronecker product singular value decomposition (TKPSVD) that decomposes a real kway 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 kway tensor. The algorithm relies on reshaping and permuting the original tensor into a dway tensor, after which a polyadic decomposition with orthogonal rank1 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 arbitrarydegree Kronecker product decomposition of tensors. Zbl 1424.15045 Batselier, Kim; Wong, Ngai 
2017

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Cited by 24 Authors
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