| 基于块循环矩阵的对称张量的最佳秩-1逼近 |
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| 引用本文： | 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. |
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| 作者姓名： | 徐娇娇 杨志霞 蒋耀林 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金（No.11561066） |
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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.
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| 关 键 词： | 对称张量 秩-1张量 最佳秩-1逼近 |
| 收稿时间： | 2017-04-26 |
The best rank-one approximation of the symmetric tensor based on the block circulant matrix |
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| XU Jiaojiao,YANG Zhixia,JIANG Yaolin.The best rank-one approximation of the symmetric tensor based on the block circulant matrix[J].OR Transactions,2019,23(1):53-60. |
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| Authors: | XU Jiaojiao YANG Zhixia JIANG Yaolin |
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| Institution: | 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 |
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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. |
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| Keywords: | symmetric tensor rank-one tensor the best rank-one approximation |
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