基于块循环矩阵的对称张量的最佳秩-1逼近

doi:10.15960/j.cnki.issn.1007-6093.2019.01.006

Abstract

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

CLC Number:

O224

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.

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

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