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Successive Rank-One Decomposition of Higher-Order Symmetric Complex Tensors
ZHANG Zhanghui #,BAI Minru *
College of Mathematics and Econometrics, Hunan University, Changsha 410082
*Correspondence author
#Submitted by
Subject:
Funding: the Innovation Platform Open Funds of Hunan Provincial Higher Education Institutions of China（No.14K018）, Hunan Provincial Natural Science Foundation of China（No.14JJ2053）, National Natural Science Foundation of China （No.11571098）
Opened online:19 April 2017
Accepted by: none
Citation: ZHANG Zhanghui,BAI Minru.Successive Rank-One Decomposition of Higher-Order Symmetric Complex Tensors[OL]. [19 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4724791
 
 
In order to get the symmetric canonical decomposition of the higher-order symmetric complex tensors, this paper extends the successive decomposition method to the tensor case, and proposes a successive symmetric rank-one complex approximation method to decompose the higher-order symmetric complex tensors. It notes that the successive decomposition of real tensors may actually be different over the real field and the complex field. We further show that a symmetric canonical decomposition could be obtained when the method is applied to a unitary diagonalizable tensor. Numerical part analyzes the solving method of solving the sub-problem. Numerical results verify the efficiency of the proposed method.
Keywords:Operational Research and Cybernetics; symmetric tensor; complex tensor; rank-one tensor; decomposition
 
 
 

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