RA-HOOI: Rank-adaptive higher-order orthogonal iteration for the fixed-accuracy low multilinear-rank approximation of tensors
Applied Numerical Mathematics(2024)
Abstract
In this paper, we propose a novel rank-adaptive higher-order orthogonal iteration (RA-HOOI) algorithm to solve the fixed-accuracy low multilinear-rank approximation of tensors. On the one hand, RA-HOOI relies on a greedy strategy to expand the subspace, which avoids computing the full SVD of the matricization of the input tensor. On the other hand, the new rank-adaptive strategy introduced in the RA-HOOI algorithm enables the obtained truncation to be more accurate. A series of numerical experiments related to synthetic and real-world tensors are carried out to show that the proposed RA-HOOI algorithm is comparable to state-of-the-art methods in terms of both accuracy and efficiency and performs better in certain situations.
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Key words
tensor,rank-adaptive strategy,higher-order orthogonal iteration,fixed-accuracy,low multilinear-rank approximation
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