A new tensor decomposition

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24 Citations (Scopus)


A new decomposition was proposed for multidimensional arrays that generalized the singular decomposition of matrices. It inherited its better properties, making it possible to use singular value decomposition algorithms in constructing decompositions of multidimensional arrays. It was found that the number of parameters in the decomposition depended linearly on on the space dimension d and had substantially simpler and more convenient form than the recursive approach. The bound for the number of parameters in decomposition was obtained by combining theorems 1 and 2. An algorithm based on standard algorithms of linear algebra was formulated for the new decomposition.

Original languageEnglish
Pages (from-to)495-496
Number of pages2
JournalDoklady Mathematics
Issue number1
Publication statusPublished - Aug 2009
Externally publishedYes


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