A Finite Algorithm to Compute Rank-1 Tensor Approximations

We propose a noniterative algorithm, called SeROAP,1 to estimate a rank-1 approximation of a tensor in the real or complex field. Our algorithm is based on a sequence of singular value decompositions followed by a sequence of projections onto Kronecker vectors. For three-way tensors, we show that our algorithm is always at least as good as the state-of-the-art truncation algorithm, ST-HOSVD,
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in terms of approximation error. Thus, it gives a good starting point to iterative rank-1 tensor approximation algorithms. By means of computational experiments, it also turns out that for fourth order tensors, SeROAP yields a better approximation with high probability when compared to the standard THOSVD
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algorithm.