Rank-one approximation to high order tensors
Rank-one approximation to high order tensors
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DOI：
10.1137/s0895479899352045
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发表时间：
2001-11-19
影响因子：
1.5
通讯作者：
Golub, GH
中科院分区：
文献类型：
--
作者：
Zhang, T;Golub, GH
奇异值分解（SVD）在工程和统计领域得到了广泛的应用。这种方法最初是由Eckart和Young在[Psychometrika， 1 (1936), pp. 211-218]中发现的，他们在那里考虑了矩阵的低秩逼近问题。SVD的一个自然推广是高阶张量的低秩逼近问题，我们称之为多维SVD。在本文中，我们研究了这种分解的某些性质以及数值算法。
The singular value decomposition (SVD) has been extensively used in engineering and statistical applications. This method was originally discovered by Eckart and Young in [Psychometrika, 1 (1936), pp. 211-218], where they considered the problem of low-rank approximation to a matrix. A natural generalization of the SVD is the problem of low-rank approximation to high order tensors, which we call the multidimensional SVD. In this paper, we investigate certain properties of this decomposition as well as numerical algorithms.