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Constructive TT-representation of the tensors given as index interaction functions with applications

Gleb Ryzhakov · Ivan Oseledets

MH1-2-3-4 #142

Keywords: [ Combinatorial problems ] [ Discrete multivariate functions ] [ Tensor train decomposition ] [ TT-Tucker format ] [ Tensor approximation ] [ game theory ] [ Theory ]


This paper presents a method to build explicit tensor-train (TT) representations. We show that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining, in many cases, optimal TT-ranks. Numerical experiments show that our method outperforms the existing ones in several practical applications, including game theory problems. Theoretical estimations of the number of operations show that in some problems, such as permanent calculation, our methods are close to the known optimal asymptotics, which are obtained by a completely different type of methods.

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