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.

中文翻译：

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RA-HOOI：张量固定精度低多线性秩近似的秩自适应高阶正交迭代

在本文中，我们提出了一种新颖的秩自适应高阶正交迭代（RA-HOOI）算法来解决张量的固定精度低多线性秩近似。一方面，RA-HOOI依靠贪婪策略来扩展子空间，这避免了计算输入张量矩阵化的完整SVD。另一方面，RA-HOOI算法中引入的新的排名自适应策略使得获得的截断更加准确。一系列与合成张量和真实张量相关的数值实验表明，所提出的 RA-HOOI 算法在准确性和效率方面可与最先进的方法相媲美，并且在某些情况下表现更好。