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

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