HOSVD-ALS

<b>Introduction</b>The truncated Tucker decomposition, also known as the truncated higher-order singular value decomposition (HOSVD), has been extensively utilized as an efficient tool in many applications. Popular direct methods for truncated HOSVD often suffer from the notorious intermediate data explosion issue and are not easy to parallelize. To handle these issues, we proposed a class of alternating least squares (ALS) based algorithms for HOSVD. The proposed methods are able to eliminate the redundant computations of the singular vectors of intermediate matrices and are therefore free of data explosion. Also, the new methods are more flexible with adjustable convergence tolerance and are intrinsically parallelizable on high-performance computers. The link of our paper is https://arxiv.org/abs/2004.02583.<br><b>Data sets</b>We provide three groups of test tensors and the corresponding numerical results.1. Randomly generated low rank dense tensors with Gaussian noise.2. Randomly generated sparse tensors.3. Tensors generated from the simulation results of a lid-driven cavity flow.You can view all of these from 'data_sets.rar' and 'results.rar'.