412
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RWTH Publication No: 443048 2014   IGPM412.pdf |
TITLE |
Convergence of Alternating Least Squares Optimisation for Rank-One Approximation to High Order Tensors |
AUTHORS |
Mike Espig, Aram Khachatryan |
ABSTRACT |
The approximation of tensors has important applications in various disciplines, but it remains an
extremely challenging task. It is well known that tensors of higher order can fail to have best
low-rank approximations, but with an important exception that best rank-one approximations
always exists. The most popular approach to low-rank approximation is the alternating least
squares (ALS) method. The conver- gence of the alternating least squares algorithm for the
rank-one approximation problem is analysed in this paper. In our analysis we are focusing on the
global convergence and the rate of convergence of the ALS algorithm. It is shown that the ALS
method can converge sublinearly, Q-linearly, and even Q-superlinearly. Our theoretical results are demonstrated on explicit examples.
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KEYWORDS |
tensor format, tensor representation, tensor network, alternating least squares optimisation, orthogonal projection method |
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