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运筹学学报 >

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

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

运筹学

基于块循环矩阵的对称张量的最佳秩-1逼近

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  • 1. 新疆大学 数学与系统科学学院, 乌鲁木齐 830046;
    2. 西安交通大学 数学与统计学院, 西安 710049

收稿日期: 2017-04-26

  网络出版日期: 2019-03-15

基金资助

国家自然科学基金（No.11561066）

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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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摘要

对称张量的最佳秩-1问题是张量研究中非常重要的部分.首先，基于三阶张量的块循环矩阵，提出了求解对称张量最佳秩-1逼近问题的一个新方法.其次，针对求解对称张量的最佳秩-1逼近方法，给出了对称张量的最佳秩-1逼近不变性的一个充要条件，以及逼近误差上界的估计.最后，数值算例表明了上述方法的可行性和误差上界的正确性.

关键词： 对称张量; 秩-1张量; 最佳秩-1逼近

本文引用格式

徐娇娇, 杨志霞, 蒋耀林 . 基于块循环矩阵的对称张量的最佳秩-1逼近[J]. 运筹学学报, 2019 , 23(1) : 53 -60 . DOI: 10.15960/j.cnki.issn.1007-6093.2019.01.006

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

参考文献

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