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,2 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 THOSVD3 algorithm.
IEEE Signal Processing Letters