On the best rank-1 and rank-(R1,R2,...,RN) approximation of higher-order tensors
On the best rank-1 and rank-(R1,R2,...,RN) approximation of higher-order tensors
复制标题
DOI：
10.1137/s0895479898346995
复制
发表时间：
2000-05-16
影响因子：
1.5
通讯作者：
Vandewalle, J
中科院分区：
文献类型：
--
作者：
De Lathauwer, L;De Moor, B;Vandewalle, J
本文讨论了矩阵的最佳秩R逼近问题的多线性推广，即在最佳最小二乘意义下，用一个预先给定列秩值、行秩值等的张量逼近一个给定的高阶张量。然而，这种方法没有直接的多线性对应物。我们讨论了幂方法和正交迭代方法的高阶推广。
In this paper we discuss a multilinear generalization of the best rank-R approximation problem for matrices, namely the approximation of a given higher-order tensor, in an optimal least-squares sense, by a tensor that has prespecified column rank value, row rank value, etc. For matrices, the solution is conceptually obtained by truncation of the singular value decomposition (SVD); however, this approach does not have a straightforward multilinear counterpart. We discuss higher-order generalizations of the power method and the orthogonal iteration method.