On the successive supersymmetric rank‐1 decomposition of higher‐order supersymmetric tensors
On the successive supersymmetric rank‐1 decomposition of higher‐order supersymmetric tensors
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DOI：
10.1002/nla.537
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发表时间：
2007-08
影响因子：
4.3
通讯作者：
Yiju Wang;Liqun Qi
中科院分区：
文献类型：
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作者：
Yiju Wang;Liqun Qi
本文考虑了一个真实的高阶超对称张量的连续超对称秩1分解.为了获得这样的分解，我们设计了一种基于迭代计算剩余张量的最佳超对称秩1近似的贪婪方法。我们进一步证明了当该方法应用于可正交对角化的超对称张量时，可以得到超对称正则分解，特别是当阶数为2时，该方法生成对称矩阵的特征值分解.详细的算法设计和数值结果本文报道。版权所有© 2007约翰威利父子有限公司.
In this paper, a successive supersymmetric rank‐1 decomposition of a real higher‐order supersymmetric tensor is considered. To obtain such a decomposition, we design a greedy method based on iteratively computing the best supersymmetric rank‐1 approximation of the residual tensors. We further show that a supersymmetric canonical decomposition could be obtained when the method is applied to an orthogonally diagonalizable supersymmetric tensor, and in particular, when the order is 2, this method generates the eigenvalue decomposition for symmetric matrices. Details of the algorithm designed and the numerical results are reported in this paper. Copyright © 2007 John Wiley & Sons, Ltd.