ORIGINAL PAPER

On the Complexity of Finding Tensor Ranks

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  • 1 Department of Mathematics, Iowa State University, 411 Morrill Road, Ames, IA 50011-2104, USA;
    2 Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA

Received date: 2020-02-17

  Revised date: 2020-11-19

  Online published: 2021-05-26

Abstract

The purpose of this note is to give a linear algebra algorithm to fnd out if a rank of a given tensor over a feld $\mathbb{F}$ is at most k over the algebraic closure of $\mathbb{F}$, where k is a given positive integer. We estimate the arithmetic complexity of our algorithm.

Cite this article

Mohsen Aliabadi, Shmuel Friedland . On the Complexity of Finding Tensor Ranks[J]. Communications on Applied Mathematics and Computation, 2021 , 3(2) : 281 -289 . DOI: 10.1007/s42967-020-00103-4

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