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Operations Research Transactions >

2019 , Vol. 23 >Issue 1: 53 - 60

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2019.01.006

The best rank-one approximation of the symmetric tensor based on the block circulant matrix

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  • 1. College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, China;
    2. College of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

Received date: 2017-04-26

  Online published: 2019-03-15

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Abstract

In this paper we mainly study the best rank-one approximation problem of a symmetric tensor. This problem plays an important role in our investigation of the tensor. Firstly, we propose a new method to solve the best rank-one approximation problem of a symmetric tensor, which is based on the block circulant matrix of a third-order tensor. Secondly, sufficient and necessary conditions and an estimation of error upper bound are provided for the best rank-one approximation method. Finally, the numerical example is presented to illustrate the feasibility of our approach and the correctness of the error upper bound.

Key words： symmetric tensor; rank-one tensor; the best rank-one approximation

Cite this article

XU Jiaojiao, YANG Zhixia, JIANG Yaolin . The best rank-one approximation of the symmetric tensor based on the block circulant matrix[J]. Operations Research Transactions, 2019 , 23(1) : 53 -60 . DOI: 10.15960/j.cnki.issn.1007-6093.2019.01.006

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